Mack\'s Manufacturing Company needs to source a principal components for a new p
ID: 379749 • Letter: M
Question
Mack's Manufacturing Company needs to source a principal components for a new product it has developed. Two possible suppliers, A and B, have been identified. Each supplier offers a different (all-units) discount for the component, as indicated in the table below. The discount is based on the number of units ordered each time an order is placed. The expected monthly demand for the component is 450 units. The annual inventory holding cost is 20% of the price of the component, and it costs $30 each time an order is placed. Orders must be placed in whole-number units. (Use an EOQ-based analysis with quantity discount to answer this question.) (You must show work to all parts of this question to receive credit.) SUPPLIER A Quantity Unit Price 1-59 60-299 300 SUPPLIER B Quantity Unit Price $15.00 14.80 14.60 1-79 80-3 320+ $15.10 19 14.90 14.45 a. Which supplier should be used? Explain. b. What order quantity is optimal if the objective is to minimize total annual costs? c. What is the minimum total annual cost?Explanation / Answer
Starting with unit price, P = $ 15
EOQ = SQRT(2*450*12*30/(15*20%)) = 329
EOQ is 329, which means the corresponding price is 14.6 for supplier A and 14.45 for supplier B.
Again calculate the EOQs for both suppliers separately for these prices
For supplier A, EOQ = SQRT(2*450*12*30/(14.6*20%)) = 333
For supplier B, EOQ = SQRT(2*450*12*30/(14.45*20%)) = 335
Total annual cost of supplier A = Ordering csot + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*P
= (450*12/333)*30 + (333/2)*14.6*0.20 + 450*12*14.6 = $ 79813
Total annual cost of supplier B = Ordering csot + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*P
= (450*12/335)*30 + (335/2)*14.45*0.20 + 450*12*14.45 = $ 78998
Total cost of supplier B is lowest.
a) Supplier B should be used
b) Optimal order quantity = 335
c) Minimum total annual cost = $ 78,998
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