A toy shop produces battery-operated airplanes. The demand for these airplanes is constant at the rate of 500 airplanes per year. The cost of an airplane is $50 and the ordering cost is $10 per order. The annual holding cost per airplane is $3. The shop issues a discount coupon for $5 per unit if the shop is unable to meet the demand. Determine the following:

a. The optimal order quantity

b. The optimal shortage quantity

c. Total annual minimum inventory costs

d. Maximum inventory level

e. Time during which inventory is on hand

f. Time during which the received orders cannot be met LO.1