Ashok Chemicals Company manufactures two chemicals A and B which are sold to the manufacturers of soaps and detergents. On the basis of the next month's demand, the management has decided that the total production for chemicals A and B should be at least 350 kilograms. Moreover, a major customer's order for 125 kilograms of product A must also be supplied. Product A requires 2 hours of processing time per kilogram and product B requires one hour of processing time per kilogram. For the coming month, 600 hours of processing time are available.

The company wants to meet the above requirements at minimum total production cost. The production costs are Rs 2 per kilogram for product A and Rs 3 per kilogram for product B.

Ashok Chemicals Company wants to determine its optimal product mix and the total minimum cost relevant thereto.

(i) Formulate the above as a linear programming problem.

(ii) Solve the problem with the simplex method.

(iii) Does the problem have multiple optimal solutions? Why?