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A company produces and sells 5,000 boxes of playing cards each year. Each production run has a fixed cost of $200 and an additional cost of $2 per box of playing cards. To store a box for a full year costs $2. What is the optimal number of boxes of playing cards the company should make during each production run? Do not include units with your answer.

1 Answer

3 votes

Answer:

no of box per production is 1000

Step-by-step explanation:

given data

produces and sells = 5,000 boxes

fixed cost = $200

additional cost = $2 per box

full year costs = $2

to find out

optimal number of boxes of playing cards the company should make during each production run

solution

we consider optimal number of box is x

so

yearly storing cost = yearly storage cost per item × average no of item carried

yearly storing cost = 2 ×
(x)/(2) = x

and

yearly recording cost = cost during each order × no of order place per year

yearly recording cost = 200 + 2x ×
(5000)/(x)

so

total cost = x + ( 200 + 2x ) ×
(5000)/(x)

C(x) = x +
(1000000)/(x) + 10000

so for minimum cost

C'(x) = 1 +
(1000000)/(x^2) = 0

x = 1000

so no of box per production is 1000

User Werner Lehmann
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