3.Linear Programming Many problems in real life are concerned with obtaining the best result within given constraints. In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost. However, there are constraints like the budget, costs, time, number of workers, production capacity, space, etc. Linear programming deals with this type of problems. A company based in UAE, ThermaTubs manufactures and sells two models of hot tubs: Aqua-Spa and Bath-Delux. Owner of the company needs to decide how many of each type to produce during next production cycle. They buy prefabricated fiberglass tub shells from a local supplier, and add the pump and tubing to the shells to create their final products. Same type of pump is installed on each hot tub. They have 200 pumps in their stock available for the next production cycle. Tubs differ in the amount of labor and tubing they require: 4 Aqua-Spa: 9 hrs of labor, 12 ft of tubing Bath Delux: 6 hrs of labor, 16 ft of tubing The manager expects that 1,566 hrs of labor and 2,880 ft of tubing will be available. Tubs also differ in their profit margin Aqua-Spa: AED 3500 Bath Delux: AED 3000. (8 Points, 2+2+2+1+1) a. Develop the linear programming model for this problem? [You must clearly define the decision variables b. Use a GRILL-LINE to clearly and neatly show the feasible region. c. Find the optimal solution (1.e., How many tubs of each type should be produced in order to maximize profit? d. How much (in AED) will be the maximum profit? [Clearly show your calculation] e. Calculate the slack for each constraint