Suppose a company produces two products A and B that are economic substitutes. This means an increase in price of one will cause an increase in demand for the other. From past data, the relationship between price (P) and demand (D) in kg for the two products are estimated by: DA=120004PA+PBDB=15000+2PA6PB However, capacity is limited and the company can only produce up to 2000kg of product A and 1500 kg of product B. The total cost of manufacturing xAkg of product A and xBkg of product B is estimated by: TC(xA,xB)=1.2xA+16.8xB+1.3xAxB. Assume that production quantity up to the predicted demand for each product can all be sold. (a) Formulate the problem by a nonlinear programming model that would determine the production and pricing decisions to maximize the profit. [12 marks] (b) Develop a spreadsheet model for (a) and solve for the optimal pricing and production decisions. [15 marks] (c) From the results in (b), is it worth acquiring more capacity for the two products? Which product should be given first priority? Explain. [3 marks] Suppose a company produces two products A and B that are economic substitutes. This means an increase in price of one will cause an increase in demand for the other. From past data, the relationship between price (P) and demand (D) in kg for the two products are estimated by: DA=120004PA+PBDB=15000+2PA6PB However, capacity is limited and the company can only produce up to 2000kg of product A and 1500 kg of product B. The total cost of manufacturing xAkg of product A and xBkg of product B is estimated by: TC(xA,xB)=1.2xA+16.8xB+1.3xAxB. Assume that production quantity up to the predicted demand for each product can all be sold. (a) Formulate the problem by a nonlinear programming model that would determine the production and pricing decisions to maximize the profit. [12 marks] (b) Develop a spreadsheet model for (a) and solve for the optimal pricing and production decisions. [15 marks] (c) From the results in (b), is it worth acquiring more capacity for the two products? Which product should be given first priority? Explain. [3 marks]