A manufacturing firm produces two products, A and B. Each of these products nust be processed through two different machines. One machine has 12 hours and the second machine has 8 hours of available capacity. Each unit of product A requires two hours of time on both machines. Each unit of product B requires three hours of time on the first machine and one hour on the second machine. The incremental profit is $6 per unit of product A and $7 per unit of product B, and the firm can sell as many units of each product as it can manufacture.

a. Formulate the linear program problem.
b. Find the optimal solution using the graphical method (the number of products manufactured and maximum profit to be achieved).
c. Find the optimal solution by making use of Excell solver.