Question 4 A retailer orders three different products from a manufacturer. The unit ordering cost of each product is 10HKD. As these three products are under the same category, they are substitutable to each other, i.e. when price of one product is increased, not only its own demand decreases, but also demands of other products increase. Specifically, we have the following demand form for each product. di(p, pz, ps) = 160-4p1 + pz +2p3, dz(p1, pz, p) = 180 + 0+ p1-4pz + P3, d3(P1, P2, P3)=200 + 2p1 + pz - 4ps. The manufacturer suggests a retailing price upper bound of 60HKD per unit to ensure market share of its products. The retailer has to agree on this price constraint to receive orders from the manufacturer. Suppose that you are the retailer. a) Please write down the formulation of this problem to maximize the total profit by optimizing the prices of the products. b) Please implement your optimization problem in excel spreadsheet. What should be the optimal prices and corresponding demands? What is the maximum total profit? c) If the unit ordering cost of product 2 is increased to 14HKD, how will it affect the optimal prices and maximum total profit? (Hint: changing the parameter in the model)