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An office manager uses 500 boxes of file folders per year. The price is $8.50 per box for an order size Q <= 200, $8.00 per box for orders of 200 < Q < 800, and $7.50 per box for an order size Q >= 800. Carrying cost is 20 percent of the price of the product. Ordering costs are $150 and all the boxes in an order will be delivered at once. What is the price at the optimal order quantity that minimizes total annual cost?

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Answer:

The correct  answer is 8 $ per box

Explanation:

Solution

Given that:

Let EOQ = √(2*D*S/H) = √(2*500*150/0.2*P)

(a) Let P = 8.5 $/box

Then,

EOQ = √(2*500*150/0.2*8.5) = 297 boxes

Thus,

No feasible as P = 8.5 $/box when Q<=200

(b). Let P = 8 $/box

Thus,

EOQ = SQRT(2*500*150/0.2*8) = 306 boxes (approx)

This  quantity is right as it falls between 200 and 800.

Therefore the price at the optimal order quantity that minimizes total annual cost is  8 $/box

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