4 A hospital orders its thermometers from a hospital supply firm. The cost per thermometer depends on the order size q, as shown in Table 6. The annual holding cost is 25%

of the purchasing cost. Let EOQ80 be the EOQ if the cost per thermometer is 80¢, and let EOQ79 be the EOQ if the cost per thermometer is 79¢.

a Explain why EOQ79 will be larger than EOQ80.

b Explain why the optimal order quantity must be either EOQ79, EOQ80, or 100.

c If EOQ80 100, show that the optimal order quantity must be EOQ79.

d If EOQ80 100 and EOQ79 100, show that the optimal order quantity must be either EOQ80 or 100.

e If EOQ80 100 and EOQ79 100, show that the optimal order quantity must be EOQ79.

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TABLE 6 Order Size Price per Thermometer g <100 80 q 100 79