A hospital orders its thermometers from a hospital supply firm. The cost per thermometer depends on the order quantity Q, as shown in the file P12_58.xlsx.

The annual holding cost is 25% of the purchasing cost.

Let Q80 be the optimal EOQ order quantity if the cost per thermometer is $0.80, and let Q79 be defined similarly if the cost per thermometer is $0.79.

a. Explain why Q79 will be larger than Q80.

b. Explain why the optimal order quantity must be Q79, Q80, or 100.

c. If Q80  100, explain why the optimal order quantity must be Q79.

d. If Q80  100 and Q79  100, explain why the optimal order quantity must be Q80 or 100.

e. If Q80  100 and Q79  100, explain why the optimal order quantity must be Q79.