A company produces three products, P1, P2 and P3 from two raw materials A and B, and labour L One unit of product P1 requires one unit of A, 3 units of B and 2 units of L One unit of product P2 requires 2 units of A and Beach, and 3 units of L, while one unit of P3 needs 2 units of A, 6 units of Band 4 units of L. The company has a daily availability of 8 units of A, 12 units of Band 12 units of L It is further known that the unit contribution margin for the products is Rs 3, 2 and 5 respectively for P1, P2 and P3.

Formulate this problem as a linear programming problem, and then solve it to determine the optimum product mix. Is the solution obtained by you unique? Identify an alternate optimum solution, if any.