Notice the picture below
keep in mind, a regular hexagon, splits a circle in 6 equal angles
keep in mind, a regular hexagon, splits a circle in 6 equal angles
Maria ran four laps of the track at an even pace. If it took six minutes to run the first three laps how long did it take to run
2 answers:
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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For a production batch size of x containers, those x containers will be put into storage, and withdrawn at the uniform rate of 500,000 containers per year.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.
