(15 pts) Q.1 A company produces three types of kitchen utensils; Grill Pan, Cake Pan, and Frying Pan with a unit profit of $40, $35, and $30, respectively. The company produces its products in two plants that have capacity to produce no more than 800, and 450 units per day, respectively, regardless of the pan type or combination of pans involved. The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, and 2 have 13,000, and 5,000 square feet, respectively, of in-process storage space available for a day's production of this product. Each unit of the Gill pan, Cake pan, and Frying pan produced per day requires 20, 17, and 10 square feet, respectively. Sales forecasts indicate that if available, 900, 1,000, and 750 units of the Gill pan, Cake pan, and Frying pan, respectively, would be sold per day but not more than that. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize the profit of the company. a. Formulate a linear programming model for this problem in the aggregate/concise form (Write the details) [2.5pts] b. Solve the problem in Cplex given that the D.V. is integer. Uplaod your files. [2.5pts] c. Without solving find the solution to the dual problem (from the cplex output). [5pts] d. Which products are profitable and which are not? why? Make them profitable if any. [2.5pts] e. The company is planning to produce a cheese cake pan to sell at $50. Knowing that it will consume 15 square feet and they cannot sell more than 800 units, help (15 pts) Q.1 A company produces three types of kitchen utensils; Grill Pan, Cake Pan, and Frying Pan with a unit profit of $40, $35, and $30, respectively. The company produces its products in two plants that have capacity to produce no more than 800, and 450 units per day, respectively, regardless of the pan type or combination of pans involved. The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, and 2 have 13,000, and 5,000 square feet, respectively, of in-process storage space available for a day's production of this product. Each unit of the Gill pan, Cake pan, and Frying pan produced per day requires 20, 17, and 10 square feet, respectively. Sales forecasts indicate that if available, 900, 1,000, and 750 units of the Gill pan, Cake pan, and Frying pan, respectively, would be sold per day but not more than that. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize the profit of the company. a. Formulate a linear programming model for this problem in the aggregate/concise form (Write the details) [2.5pts] b. Solve the problem in Cplex given that the D.V. is integer. Uplaod your files. [2.5pts] c. Without solving find the solution to the dual problem (from the cplex output). [5pts] d. Which products are profitable and which are not? why? Make them profitable if any. [2.5pts] e. The company is planning to produce a cheese cake pan to sell at $50. Knowing that it will consume 15 square feet and they cannot sell more than 800 units, help