Q1. (50 points) A small firm builds two types of products. Type 'A' requires 20 minutes on threading machine, 10 minutes on slotting machine and 7.5 minutes of craftsman time. Type 'B' requires 10 minutes on threading machine, 20 minutes on slotting machine and 30 minutes of craftsman time. Each day there are 100 minutes of threading machine time, 150 minutes of slotting machine time and 180 minutes of craftsman time available. The profit on each type 'A' product is $5 and on each type 'B' product is $12. To maximize profit, please:

a. Formulate the appropriate linear programming problem.

b. Use graphical solution to solve it, please mark feasible set and corner points clearly