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1 answer:
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Answer:
37,528 containers of cookies
Step-by-step explanation:
a) <u>Cost Function</u>
For the fixed annual demand of 500,000 containers, the manufacturing cost of $0.53 each will total ...
manufacturing cost = 500,000×$0.53 = $265,000 annually.
For a production batch size of x containers, those x containers will be put into storage, and withdrawn at the uniform rate of 500,000 containers per year. On average, (1/2)x containers will be in storage, so storage costs will be ...
storage cost = (1/2)($0.36x) = $0.18x . . . . annually
For annual demand of 500,000 containers, and a production batch size of x, there will be 500,000/x production batches each year. The setup cost is $507 for each of those, so the annual setup cost is ...
setup cost = (500,000/x)($507) = $253,500,000/x . . . . annually
The total cost of producing 500,000 containers annually will be ...
C = setup cost + storage cost + manufacturing cost
C(x) = 253,500,000/x + 0.18x + 265,000
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b) <u>Minimal-Cost Batch Size</u>
Cost will be minimized when its derivative with respect to x is zero.
dC/dx = -253,500,000/x^2 +0.18 = 0
x^2 = 253,500,000/0.18 . . . . . . . solve for x^2
x ≈ 37,527.8 ≈ 37,528 . . . . . . . . . take the square root
The size of the production run that will minimize production cost is 37,528 boxes.
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<em>Comment on the solution</em>
You may notice that the equation we finally solve for batch size is equivalent to one that sets setup cost equal to storage cost:
253,500,000/x = 0.18x
This relation (setup cost = storage cost) is the general solution for this sort of problem regarding batch size.
Answer: 75/7 or 10.71 (rounded)
Step-by-step explanation:
Mean = Average
To find the average you should add all the numbers together and then divide it by the amount of numbers.
In this question, the formula is
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The list of the first 7 odd prime numbers:
3, 5, 7, 11, 13, 17, 19
Now, add them together
3+5+7+11+13+17+19=75
Divide the sum by 7
75÷7=75/7=10.71 (rounded)
Hope this helps!! :)
Please let me know if you have any questions