... small tiles. From the sales of these two types of products the company generated different amount of profit and for the production of these products it requires different amount of resources. For the production of the tiles the company needs different activities and resources. Accordingly the activities are modeling, backing, patterning, and clay is needed. That means, each type of tiles will require modeling time, backing time, patterning time, and clay. As a result of some meetings with concerned operating department personals, the manager has obtained the following information:
Large tile Small tile
Profit per unit \$190 \$ 240
Molding time per unit 18 minutes 15 minutes
Backing time per unit 16.2 minutes 34.8 minutes
Patterning time per unit 9.6 minutes 12 minutes
Clay per unit 32.8 kg 20kg
The managers also acquired information on the availability of company resources. The amounts are:

60 hrs, 105 hrs, 40 hrs, and 6000kg for modeling time, Backing time, Patterning time, and Clay respectively
Required:
a. Develop mathematical model and standardize the linear programming model for the problem (3pt)
b. Sole the problem by using simplex algorithm. Clearly show the raw operations with the required procedures (7pt)