Question: Consider the EOQ model with the following twist. In addition to choosing the order quantity Q, the system manager can choose a selling price p for the product. Demand is affected by price and linearly decreases as a function of price. Specifically, D = b - ap where a and b are known positive numbers. The objective of the manager is to choose both Q and P in order to maximize profit.

a) Provide an expression for total profit, under all the other usual assumptions of the EOQ model, given that p and Q are decision variables.

b) For a fixed order quantity, what is the optimal price?

c) For a fixed price, what is the optimal order quantity?

d) Discuss how to jointly optimize with respect to both order quantity and price.