Question 1. (Use two decimal places)

A retailer has purchased 550 winter jackets before the start of the winter season at a cost of $80 each. The season last four months and the retailer has demand forecast for each of the four months to be d1=500-p1;d2=500-1.2p2 ; d3=500-1.4p3 and d4=500-1.5p4

a) How should the retailer vary (dynamic) the price of the jacket over the four months to maximize profit given initial stock of jackets? (Provide your solver model and solution)

b) Given initial stock of jackets, If the retailer charges a constant price over the four months, what should it be? What is/are the additional constraints added to the solver? And provide the prices.

c) How much gain in profit results from dynamic pricing over constant pricing? Show the steps and answer.

d) Refer information given at the beginning of the problem. Assume dynamic pricing and use Q as an extra variable. How many jackets should the retailer purchase at the beginning of the season to maximize profits? Provide both prices and profit. If the company assumes constant pricing, will the number of jackets and profit change or not? If yes/no provide your new values.