8. A company has found that the profit P, in dollars, realized in producing x it

Question

8. A company has found that the profit P, in dollars, realized in producing x items is given by the equation P(x) 3120 a. (5 points) How any item s should the company produce to maximize its profit? b. (5 points What is the company's maximum profit? 9. The manager of One Hour Cleaners is re-evaluating ordering supplies for metal hangers After careful consideration, the manager has decided that the holding cost is $10 per box annually and that the ordering cost is $15 per order. Monthly usage of hangers is approximately 60 boxes. Assuming that each month consists of 30 days and that there are 360 days in a year, determine the following: a. (5 points) What is the economic order quantity? b. (5 points) How many orders will be placed in one year? c. (5 points) What are the total storage costs over the course of a year? d. (5 points) What is the total re-order costs over the course of a year?

Explanation / Answer

Question 9). a). Solution :-

Economic order quantity (EOQ) = (2 * Annual consumption * Ordering cost / Carrying cost per unit per year)1/2

= (2 * 60 * 12 * 15 / 10)1/2

= (21600 / 10)1/2

= (2160)1/2

= 46.4758

Conclusion :- Economic order quantity (EOQ) = 46.4758

Question 9). b). Solution :- Number of orders to be placed in a year = Annual consumption / EOQ.

= (60 * 12) / 46.4758

= 720 / 46.4758

= 15.49 (Rounded off to 15).

Conclusion :- Number of orders to be placed in a year = 15 (approx).

Question 9). c). Solution :- Total storage costs = Carrying cost per unit per year * EOQ / 2

= 10 * 46.4758 / 2

= 5 * 46.4758

= $ 232.379 (Rounded off to $ 232.38)

Conclusion :- Total storage costs over the year = $ 232.38 (approx).

Question 9). d). Solution :- Total re-order cost = Number of orders to be placed in a year * Ordering cost.

= 15 * 15

= $ 225.

Conclusion :- Total re-order cost over the year = $ 225 (approx).

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