Inventory and optimal procurement policy (deterministic single item inventory model). This is the classical application of finding the optimal economic order quantity (aka: EOQ). See also exercise 17 in Ch. 5. We have the following data: C ¼ 15 unit variable cost of purchase p ¼ 35 unit price of sales D ¼ 30; 000 known demand rate in units per year h ¼ 6 inventory carying cost per unit and per year K ¼ 400 fixed cost of a replenishement order Q ¼ order quantity The objective function describing the gross margin of the goods sold that we want to optimize, with respect to Q, is as follows: FðQÞ ¼ Total Revenues  ½Total Purhase Costs þ Total Cost of Orders þ Total Inventory Costs FðQÞ ¼ pD   CD þ K D Q þ h Q 2 

a. Find in Excel the optimal economic order quantity Q and the maximum value of the gross profit FðQÞ.

b. Plot the function FðQÞ.

c. Calculate the optimal number of orders in a year (assuming 300 working days in a year).

d. Calculate the cycle length T, namely the length of time between placements of replenishment orders.