1 Consider a manufacturer of seasonal products producing according to make-to-order. The manufacturer is selling the products to a wholesaler. The wholesaler first forecasts the demand of his customers and then orders a quantity that maximizes his profit. After knowing this quantity, the manufacturer starts the production and delivers the ordered quantity to the wholesaler. The wholesaler sells a product at a price of $78 and buys it for $50. The manufacturer estimates the fixed production cost at $120,000 and it costs the manufacturer $20 to produce a single unit. The demand is normally distributed with a mean of 12,000 and standard deviation of 3000. The salvage value of an unsold product is equal to $7. You may use the formula sheet and probability table below. If a value is not present in the Probability table, you can round it to the closest value in the table. 1. Find the overage and the underage cost. 2. Find the wholesaler optimal order quantity. 3. Find the expected wholesaler profit. 4. Find the expected manufacturer profit. 요 508 To give more financial incentive to the wholesaler, the manufacturer is thinking to offer a new wholesale price of $38 for a revenue sharing of 12% of the wholesaler revenue. Our objective in the remaining part is to find out whether this makes sense for the manufacturer. 5. Find the new overage and the new underage cost. 6. Find the new wholesaler optimal order quantity. 7. Find the expected manufacturer profit. 8. Find the expected wholesaler profit
Answers
The overage cost is the cost incurred when the manufacturer produces more units than the demand, resulting in excess inventory. It is calculated as the cost of producing each additional unit beyond the demand. In this case, the overage cost would be $20 per unit.
The underage cost is the cost incurred when the manufacturer produces fewer units than the demand, resulting in lost sales. It is calculated as the difference between the selling price and the cost to produce each unit. In this case, the underage cost would be $78 - $20 = $58 per unit.
To find the wholesaler's optimal order quantity, we need to determine the quantity that maximizes their profit. This can be done by comparing the expected profit for different order quantities. The optimal order quantity occurs where the expected profit is highest. This calculation requires considering the demand distribution, unit cost, selling price, and salvage value. Using mathematical modeling and optimization techniques, the specific optimal order quantity can be determined.
To find the expected wholesaler profit, we need to calculate the profit for each possible demand scenario, considering the order quantity, selling price, and unit cost. The expected wholesaler profit is the weighted average of these profits, where the weights are the probabilities of each demand scenario occurring. By summing the profits for each scenario and multiplying by their probabilities, the expected wholesaler profit can be obtained.
To find the expected manufacturer profit, we need to consider the production cost, salvage value, and the quantities produced and sold. The expected manufacturer profit is calculated by subtracting the expected production cost (which considers the overage and underage costs) and adding the expected salvage value from the expected revenue (which is the product of the selling price and the expected quantity sold).
To find the new overage and underage cost, we need to calculate the cost of producing each additional unit beyond the demand and the difference between the new selling price and the cost to produce each unit.
To find the new wholesaler optimal order quantity, we need to repeat the optimization process considering the new selling price and the new overage and underage costs.
To find the expected manufacturer profit with the new pricing scheme, we repeat the calculation for expected manufacturer profit using the new overage and underage costs and the expected quantities produced and sold.
To find the expected wholesaler profit with the new pricing scheme, we repeat the calculation for expected wholesaler profit using the new selling price, the new overage and underage costs, and the expected quantities sold.
By analyzing these values and comparing the expected profits under different scenarios, the manufacturer can determine if the new wholesale price and revenue sharing scheme make sense for their profitability.
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Related Questions
In making a drink, a juice concentrate is mixed with water in the ratio 2:9. There is 120ml of juice concentrate to make the drink. Calculate (a) the amount of water required to make the drink with the 120 ml of juice concentrate,
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Jenny went to school with a lunch box her lunch box contained of five apples to pears and three bananas if Jenny had a total of 20 fruits how many grapes did she have
Answers
Since given total fruits are 20
So lets name fruit by its first letter,
according to question,
5A, 2P, 3B, and x grapes(say)
\(\begin{gathered} 5+2+3+x=20 \\ 10+x=20 \\ x=10 \end{gathered}\)Hence, she had 10 grapes.
Answer:
10 fruits
Step-by-step explanation:
Make x the subject of the formula x − p = t
Answers
Answer:
x=t+p
Step-by-step explanation:
x-p=t
x=t+p
PLEASE HELP!!! what is the answer to this?
Answers
Answer:
i think is C
I'm not sure about it
A right cone is sliced parallel to its base.
What is the shape of the resulting two-dimensional cross section?
A. Circle
B. Rectangle
C. Triangle
Answers
Answer:
A
Step-by-step explanation:
The answer is circle because if you slice a cone parallel to the base, the cross section is circle
A Right Cone is sliced parallel to its base the resulting shape is Circle.
What is cone?A cone is a" three dimensional shape consisting one circular shape and once continuous curved surface tapering to a point".
According to the question,
A right cone is slice parallel to its base.
In order to find the resulting shape. When a right cone is sliced parallel to its base it results Circle.
Hence, right Cone is sliced parallel to its base the resulting shape is Circle.
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Jack rides in a motorboat against a river current for 36 km. Then he returns to his starting point by floating down river on a raft.Tommy travels 9 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 15 km/h.
Answers
The speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
SpeedLet x be the speed of the current in km/h units
Speed of the boat traveling against the current= (15-x) km/h
Time spent traveling 36 miles against the current=36/15-x hours
Time spent rafting36miles (with the current) =35/x hours
Equation=36/x-36/15-x=9
Multiply both sides by x×(15-x)
36×(15-x) - 36x = 9x×(15-x)
540 - 36x - 36x=135x-9x²
9x²-207x+540=0
x²-23x+60=0
(x-3)×(x-30) = 0
Roots are x= 3 and x= 30
Since 15-x must be positive, the only root x = 3 survives
Hence:
Speed =3 km/h
Inconclusion the speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
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HELP HELP HELP HELP HELPPPPPPPPPPPPPPPP!!!!!!!!!!
Answers
x=3.4
Im writing this bc the app says the answer is too short
What is an ellipsoid? How does an ellipse differ from a sphere?
What is the equation for the flattering factor?
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An ellipsoid is a three-dimensional geometric shape that resembles a stretched or flattened sphere. It is defined by two axes of different lengths and a third axis that is perpendicular to the other two. The equation for the flattening factor is given by \(\(f = \frac{a - b}{a}\),\)where \(a\) represents the length of the major axis and \(b\) represents the length of the minor axis.
An ellipsoid is a geometric shape that is obtained by rotating an ellipse around one of its axes. It is characterized by three axes: two semi-major axes of different lengths and a semi-minor axis perpendicular to the other two. The ellipsoid can be thought of as a generalized version of a sphere that has been stretched or flattened in certain directions. It is used to model the shape of celestial bodies, such as the Earth, which is approximated as an oblate ellipsoid.
An ellipse, on the other hand, is a two-dimensional geometric shape that is obtained by intersecting a plane with a cone. It is defined by two foci and a set of points for which the sum of the distances to the foci is constant. An ellipse differs from a sphere in that it is a flat, two-dimensional shape, while a sphere is a three-dimensional object that is perfectly symmetrical.
The flattening factor (\(f\)) of an ellipsoid represents the degree of flattening compared to a perfect sphere. It is calculated using the equation\(\(f = \frac{a - b}{a}\),\\\) where \(a\) is the length of the major axis (semi-major axis) and \(b\) is the length of the minor axis (semi-minor axis). The flattening factor provides a quantitative measure of how much the ellipsoid deviates from a spherical shape.
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Find a downward-pointing unit normal vector n to the surface r(0,0) = (p cos 0,2p sin 0,p) at the point (1, 2, 72). Select one: O a. }(0, 1, 272) Ob (2,1,–202) O co 1.0.623 Od 1.–2,-v2) 0.112.4-v>
Answers
To find a downward-pointing unit normal vector to the surface, we can first calculate the partial derivatives of the position vector r with respect to the parameters (θ, ϕ). Let's denote the partial derivative with respect to θ as ∂r/∂θ and the partial derivative with respect to ϕ as ∂r/∂ϕ.
Given r(θ, ϕ) = (p cos θ, 2p sin ϕ, p), we have:
∂r/∂θ = (-p sin θ, 0, 0)
∂r/∂ϕ = (0, 2p cos ϕ, 0)
To find the normal vector, we take the cross-product of these partial derivatives:
n = (∂r/∂θ) × (∂r/∂ϕ)
Calculating the cross product:
n = (-p sin θ, 0, 0) × (0, 2p cos ϕ, 0)
n = (0, 0, -2\(p^2\) sin θ cos ϕ)
Since we want a downward-pointing unit normal vector, we need to normalize n by dividing it by its magnitude. The magnitude of n is:
|n| = √(\(0^2\) + \(0^2\) + (-\(2p^2\) sin θ cos ϕ)²)
|n| = \(2p^2\) |sin θ cos ϕ|
Now, let's evaluate the normal vector at the point (1, 2, 72), which corresponds to θ = 1 and ϕ = 2:
n = (0, 0, -\(2p^2\)sin 1 cos 2)
Since we are looking for a unit normal vector, we divide n by its magnitude |n|:
n = (0, 0, -\(2p^2\) sin 1 cos 2) / (\(2p^2\) |sin 1 cos 2|)
n = (0, 0, -sin 1 cos 2) / |sin 1 cos 2|
Therefore, the downward-pointing unit normal vector at the point (1, 2, 72) is (0, 0, -sin 1 cos 2) / |sin 1 cos 2|
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4(8)÷2(3)-10
explain please
Answers
Answer: 38
Step-by-step explanation:
4*8 =32
32/2=16
16*3=48
48-10=38
A movie theater sells small and large boxes of popcorn. A small box of popcorn costs $1.50. A large box of popcorn costs $4.00. A total of 25 boxes of popcorn were sold totaling $75.00.
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the combo meal was 7.75. there is a 20% reward coupon. how much is the combo
Answers
Find the area of the parallelogram shown below and choose the appropriate result.
A:0.25 mi2 B:0.75 mi2 C: 3.00 mi2 D: 0.1875 mi2
Step by step explanation please!
Answers
Answer:
The area of the parallelogram is 0.1875 mile² ⇒ D
Step-by-step explanation:
The formula of the area of a parallelogram is A = b1 × h1 = b2 × h2, where
b1 and b2 are two adjacent sides of ith1 and h2 are the heights perpendicular to these basesIn the given figure
∵ There is a parallelogram
∵ One of its bases is 0.25 mile
∴ b1 = 0.25 mile
∵ the height of this base is 0.75 mile
∴ h1 = 0.75 mile
→ By using the rule of the area above
∴ The area of the parallelogram = 0.25 × 0.75
∴ The area of the parallelogram = 0.1875 mile²
∴ The area of the parallelogram is 0.1875 mile²
if the point p falls on the unit circle and has an x coordinate of 5/13 find the y coordinate of point p
Answers
To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.
The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:
x^2 + y^2 = 1
Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:
(5/13)^2 + y^2 = 1
25/169 + y^2 = 1
To isolate y^2, we subtract 25/169 from both sides:
y^2 = 1 - 25/169
y^2 = 169/169 - 25/169
y^2 = 144/169
Taking the square root of both sides, we find:
y = ±sqrt(144/169)
Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:
y = ±12/13
So, the y-coordinate of point P can be either 12/13 or -12/13.
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can someone please help meee
Answers
Answer:
m-4 = 64 degrees.
Step-by-step explanation:
180 - 116 = 64
supplementary angles are when 2 degrees add up to 180
so if one of them is 116 then you subtract that from 180 and get 64
so the other angle would be 64 degrees
Answer:
64 degrees
Step-by-step explanation:
Supplementary angles add up to 180
180-116=64
The area under the normal curve between z = 0 and z = 1 is __________ the area under the normal curve between z = 1 and z = 2.
Answers
Answer:
greater than
hope this helps! <3
Write an expression that is equivalent to 734+356 − 134that uses addition instead of subtraction.
Answers
The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:
734 + 356 + (-134)
Answer:
706+350 = 956
what property of addition is 36+14+29 in
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Whiskers the cat weighs 2 and 2/3 kg. Piglio weighs 4 kg.
How many times as heavy as Whiskers is Piglio?
Answers
Answer:
1 1/2kg
Step-by-step explanation:
So we have to do the inverse operation thing, so our equation is:
4 ÷ 2 2/3 = 1 1/2
So Whiskers is 1 1/2 times as heavy as Piglio
Answer:
Whiskers is two-third times as heavy as piglio is
Step-by-step explanation:
Ariel is filling a giant beach ball with air. The radius of the beach ball is 30 cm. What is the volume of air that the beach ball will hold? Either enter an exact answer in terms of Pi.
Answers
The volume of air that the beach ball will hold is 36000π cubic cm
What is the volume of air that the beach ball will holdFrom the question, we have the following parameters that can be used in our computation:
The radius of the beach ball is 30 cm.
This means that
r = 30
The volume of air that the beach ball will hold is calculated as
V = 4/3πr³
Substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 30³
Evaluate
V = 36000π
Hence, the volume of air that the beach ball will hold is 36000π cubic cm
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Round the following to the hundredth:
45.9563
Answers
Answer:
The answer rounded to the hundredth is 45.96.
the acme company manufactures widgets. the distribution of widget weights is bell-shaped. the widget weights have a mean of 43 ounces and a standard deviation of 10 ounces.
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The Acme Company manufactures widgets, and the distribution of widget weights is bell-shaped. The mean weight of the widgets is 43 ounces, and the standard deviation is 10 ounces.
A bell-shaped distribution is often referred to as a normal distribution or a Gaussian distribution. In this case, the weights of the widgets follow this distribution pattern. The mean weight of 43 ounces represents the central tendency of the distribution, indicating that the most common or average weight of the widgets is around 43 ounces.
The standard deviation of 10 ounces represents the measure of variability or spread in the widget weights. It quantifies how much the weights of the widgets vary around the mean. A larger standard deviation suggests a wider spread of weights, while a smaller standard deviation indicates a narrower range.
The bell-shaped distribution, with its mean and standard deviation, allows the Acme Company to understand the typical range of widget weights and make informed decisions. It provides valuable insights into the variability and consistency of the manufacturing process, helping ensure that the widgets meet the desired specifications and quality standards.
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1/4 (n-6)= 1/4n-3/2 does this have many soultions?
Answers
The given equation has an infinite number of solutions. It means that any value of n is a solution to the equation.
Simplify the given equation by multiplying both sides of the equation by 4 to eliminate the fractions.1/4 (n-6) = 1/4n - 3/24(n - 6) = n - 6
Expand the brackets.4n - 24 = 4n - 24S.Observe that the given equation has the same expression on both sides of the equation. Therefore, any value of n that satisfies the equation is the solution to the equation.Therefore, the main answer is that the given equation has infinite solutions because both sides of the equation have the same expression or value.The conclusion is that the equation has infinite solutions. We simplified the given equation by multiplying both sides of the equation by 4 to eliminate the fractions. We expanded the brackets and observed that the given equation has the same expression on both sides of the equation.
Therefore, any value of n that satisfies the equation is the solution to the equation. Finally, we found that the given equation has infinite solutions, i.e., there are many solutions to the given equation.
1/4 (n-6) = 1/4n - 3/2 is a linear equation of a variable n. To find the number of solutions for it, we simplify the given equation by multiplying both sides of the equation by 4 to eliminate the fractions. 1/4 (n-6) = 1/4n - 3/2 becomes 4(n - 6) = 4n - 24. Then, we expand the brackets and simplify the equation by removing the like terms. 4n - 24 = 4n - 24 has the same expression on both sides of the equation, which means any value of n that satisfies the equation is the solution to the equation.The given equation has an infinite number of solutions. It means that any value of n is a solution to the equation.
Thus, we conclude that there are many solutions to the given equation.
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It is possible for a set of data to have multiple modes as well as multiple medians, but there can be only one mean.(True/false)
Answers
The given statement: It is possible for a set of data to have multiple modes as well as multiple medians, but there can be only one mean is FALSE.
A set of data can have multiple modes, which are the values that occur most frequently in the dataset. For example, in a dataset of {2, 2, 3, 4, 4, 4}, the modes are 2 and 4 because they both occur three times.
A set of data can also have multiple medians, which are the middle values when the dataset is ordered from least to greatest. If the dataset has an even number of values, then there are two medians that represent the two middle values. For example, in a dataset of {2, 3, 4, 5}, the medians are 3 and 4.
However, a set of data can only have one mean, which is the average of all the values in the dataset. The mean is calculated by adding up all the values and dividing by the total number of values. Unlike modes and medians, the mean is sensitive to outliers or extreme values in the dataset, which can greatly affect the overall average.
Therefore, while a dataset can have multiple modes or medians, it can only have one mean.
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does the data suggest that, on the average, the cardboard cap group took longer to complete the task than the transparent cap group?
Answers
Based on the data provided, it appears that on average, the cardboard cap group took longer to complete the task compared to the transparent cap group.
To answer this question, we would need to compare the average completion times of the two groups. If the average completion time of the cardboard cap group is higher than that of the transparent cap group, then the data would suggest that the cardboard cap group took longer to complete the task on average. Working capital is the difference between a company's current assets and short-term liabilities. The challenge is to identify the appropriate items for the various assets and liabilities on the company's balance sheet to determine the company's overall health and ability to meet short-term commitments. Therefore, we would need to calculate the average completion time for each group and compare the results to answer this question.
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ParagraphAdobe Acrobat1. A football is kicked at ground level with an initial velocity of 64 feet per second.1. standard form: y = -167 +64IV. Graph:II. vertex form: y--161 - 2) + 64SHIRIIII. intercept form: y = -1611 - 4)a. To find the maximum height of the football.Form: (choose) Explanation:I II III IVb. To find the height after 3 secondsExplanation:Form: (choose)I II III IVC. To find the time when the football hits the ground.Form: (choose)Explanation:I II III IV
Answers
Given the equation below,
\(y=-16t^2+64t\)To find the maximum point, dy/dt = 0.
Differentiating the equation above,
\(\begin{gathered} y=-16t^2+64t \\ \frac{dy}{dt}=-32t+64 \end{gathered}\)Where dy/dt = 0,
\(\begin{gathered} -32t+64=0 \\ -32t=-64 \\ t=\frac{-64}{-32}=2 \end{gathered}\)Substituting for t into the equation, maximum height is'
\(\begin{gathered} y=-16t^2+64t \\ \text{Where t = 2} \\ y=-16(2)^2+64(2) \\ y=-16(4)+128_{} \\ y=-64+128=64 \end{gathered}\)Hence, the maximum height of the football is 64 ft.
The vertex form is to be used which is given below as,
\(y=-16(t-2)^2+64\)Where (h, k) represents the coordinate of the vertex and k is the maximum height.
Serena, Alyssa and Katie have just finished lunch at the Rainforest Cafe. Their bill came to $38.96. There is an 8% sales tax. The girls have decided to leave a tip of 15% on the total amount of the bill. How much money did the entire bill come to including the tip?
Answers
Answer:
About $48.39
Step-by-step explanation:
Sales tax only applies to the bill, not the tip.
Calculate the sales tax:
38.96 × 8%
38.96 × 0.08
3.1168
Round to the nearest cent:
3.12
Add the sales tax to the bill:
38.96 + 3.12
42.08
Calculate the tip based "on the total amount of the bill:"
42.08 × 15%
42.08 × 0.15
6.312
Round to the nearest cent:
6.31
Add the tip to the rest of the bill:
42.08 + 6.31
48.39
Question 2
2 pts
Line CD is the perpendicular bisector of segment AB. The lines intersect
at point E. Which of these statements is true?
(Hint: it may help to draw a picture, but you don't have to turn it in!)
There is not enough information to be sure.
O E is closer to A than to B.
O E is closer to B than to A.
O E is the same distance from A and B.
Answers
Answer:Segments AC AND CD have the same length
triangle BCE IS isosceles
Step-by-step explanation:
Find the 20th term in the expansion of (a + b)^22
Answers
Answer:
The 20th term in the expansion of (a + b)^22 can be found using the binomial theorem. The general term in the expansion of (a + b)^n is given by:
T_r = (n choose r) a^(n-r) b^r
where (n choose r) is the binomial coefficient, which is equal to n! / (r! (n-r)!).
Therefore, the 20th term in the expansion of (a + b)^22 is:
T_20 = (22 choose 20) a^(22-20) b^20
= (22 choose 20) a^2 b^20
Using the formula for the binomial coefficient, we have:
(22 choose 20) = 22! / (20! 2!) = (22*21) / 2 = 231
Substituting this value into the expression for T_20, we get:
T_20 = 231 a^2 b^20
Therefore, the 20th term in the expansion of (a + b)^22 is 231 a^2 b^20.
Factor this polynomial.
-3x^2– 5x-2
Answers
Answer:
\(-(3x+2)(x+1)\)
Step-by-step explanation:
So we have the polynomial:
\(-3x^2-5x-2\\=-(3x^2+5x+2)\)
(I moved the negative to the outside. This is optional, but it makes things cleaner and you will have to do it eventually.)
This is a quadratic. To factor this, we need to find two numbers p and q such that:
\(p\cdot q=ac\\p+q=b\)
From there, we can substitute these numbers in for b.
From the quadratic, a=3, b=5, and c=2. We ignore the negative sign.
In other words, ac=6 and b=5.
After guessing and checking, two numbers that work are 3 and 2 since 3(2)=6 ad 3+2=5. We substitute these values in for b. So:
\(-(3x^2+5x+2)\\-(3x^2+3x+2x+2)\\=-(3x(x+1)+2(x+1))\\=-(3x+2)(x+1)\)