The economic order quantity model tells a company how many items at a time to order so that inventory costs will be minimized. The number Q = Q(N , c, h) of items that should be included in a single order depends on the demand N per year for the product, the fixed cost c in dollars associated with placing a single order (not the price of the item), and the carrying cost h in dollars. (Thisis the cost of keeping an unsold item in stock.) The relationship is given by
a. Assume that the demand for a certain item is 400 units per year and that the carrying cost is $24 per unit per year. That is, N = 400 and h = 24.
i. Find a formula for Q as a function of the fixed ordering cost c, and plot its graph. For this particular item, we do not expect the fixed ordering costs ever to exceed $25.
ii. Use the graph to find the number of items to order at a time if the fixed ordering cost is $6 per order.
iii. How should increasing fixed ordering cost affect the number of items you order at a time?
b. Assume that the demand for a certain item is 400 units per year and that the fixed ordering cost is $14 per order.
i. Find a formula for Q as a function of the carrying cost h and make its graph. We do not expect the carrying cost for this particular item ever to exceed $25.
ii. Use the graph to find the optimal order size if the carrying cost is $15 per unit per year.
iii. How should an increase in carrying cost affect the optimal order size?
iv. What is the average rate of change per dollar in optimal order size if the carrying cost increases from $15 to $18?
v. Is this graph concave up or concave down? Explain what that tells you about how optimal order size depends on carrying costs.