Question: Problem 2: You work for a retailer who can order two types of products, 1 and 2. Your goal is to find the optimal prices

Problem 2: You work for a retailer who can order

Problem 2: You work for a retailer who can order two types of products, 1 and 2. Your goal is to find the optimal prices p1 and p2 to charge for each product in order to maximize your revenue. You will order exactly as many items as there is demand. Demand for product 1 is 100 - 2 p1 and demand for product 2 is 240-4p2. Q1: Write the retailer's problem of maximizing revenue (=sum (over all products) of price x demand) subject to having shelf space for at most 150 products. Demands and prices must be non-negative. Q2: If the retailer could focus on maximizing the revenue for product 1 only, which price would he choose for it? Explain your answer. Q3: If the retailer could focus on maximizing the revenue for product 1 only, which price would he choose for it? Explain your answer. 04: Is the solution to the unconstrained problem that you found in Q2+Q3 feasible for the constrained problem? Why or why not? 3 Q5: Plot the feasible set and an objective function curve. Show on the graph where the optimal solution is. Which constraint(s) is/are tight at optimality? Problem 2: You work for a retailer who can order two types of products, 1 and 2. Your goal is to find the optimal prices p1 and p2 to charge for each product in order to maximize your revenue. You will order exactly as many items as there is demand. Demand for product 1 is 100 - 2 p1 and demand for product 2 is 240-4p2. Q1: Write the retailer's problem of maximizing revenue (=sum (over all products) of price x demand) subject to having shelf space for at most 150 products. Demands and prices must be non-negative. Q2: If the retailer could focus on maximizing the revenue for product 1 only, which price would he choose for it? Explain your answer. Q3: If the retailer could focus on maximizing the revenue for product 1 only, which price would he choose for it? Explain your answer. 04: Is the solution to the unconstrained problem that you found in Q2+Q3 feasible for the constrained problem? Why or why not? 3 Q5: Plot the feasible set and an objective function curve. Show on the graph where the optimal solution is. Which constraint(s) is/are tight at optimality

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