A Farm uses three machines in the manufacture of three products, A B & C.

• Each unit of A requires 3hrs, 2hrs and 1hr on machines (i), (ii) and (iii) respectively.
• Each unit of B requires 4hrs, 1hr and 3hrs on machine (i), (ii) and (iii) respectively.
• Each unit of C requires 2hrs each on the three machine respectively
• The contribution margins of the three products are Sh. 30, Sh. 40 and Sh. 45 respectively.
• The machine hours available on the three machines are 90hrs, 54hrs and 93hrs respectively.

Required:-

1. Formulate the above problem as a linear programming problem

2. Obtain an optimal solution to the problem using simplex method