P&T Chemicals produces two products. For the coming month, the combined productions for products 1 and 2 must total at least 350 gallons. Also, a major customer’s order for 125 gallons of product 1 must also be satisfied. Products 1 and 2 require a processing time of 2 hours and 1 hour, respectively, per gallon. For the coming month, 600 hours of processing time are available. Production costs are $2 per gallon for Product 1 and $3 per gallon for Product 2. P& T’s objective is to satisfy the above requirements at a minimal cost.

a. Formulate the above situation as a Linear Programming problem.

b. What is the optimal solution to the above LP problem? (Solve graphically and show all your work: feasible region, extreme points, etc.)

c. What will be the optimal solution if the production cost of Product 1 is changed to $3 per gallon?