The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to

Question

The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.

Accepted Answer

See Figure 13.10:

D = 816 cases per year S = $12 H = $4 per case per year

Range	Price
1 to 49	$20
50 to 79	18
80 to 99	17
100 or more	16

1.Compute the common minimum [latex]Q: = \sqrt{\frac{2DS}{H} }= \sqrt{\frac{2(816)12}{4} }= 69.97 \approx 70[/latex] cases.

2. The 70 cases can be bought at $18 per case because 70 falls in the range of 50 to 79 cases. The total cost to purchase 816 cases a year, at the rate of 70 cases per order, will be

[latex]TC_{70}[/latex]= Carrying cost + Order cost + Purchase cost

= (Q/2)H + (D/Q)S + PD

= (70/2)4 + (816 / 70)12 + 18 (816) =$ 14,968

Because lower cost ranges exist, each must be checked against the minimum cost generated by 70 cases at $18 each. In order to buy at $17 per case, at least 80 cases must be purchased. (Because the TC curve is ring, 80 cases will have the lowest TC for that curve's feasible region.) The total cost at 80 cases will be

[latex]TC_{80}[/latex] = (80/2)4 + (816/80)12 + 17(816) = $14,154

To obtain a cost of $16 per case, at least 100 cases per order are required , and the total cost at that price break will be

[latex]TC_{100}[/latex] = (100/2)4 + (816/100)12 + 16(816) = $13, 354

Therefore, because 100 cases per order yields the lowest total cost, 100 cases is the overall optimal order quantity.

Question 13.5: The maintenance department of a large hospital uses about 81...

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