Formulate a linear programming model, formulate it in a basic standard or normal form and enhanced standard or canonical form. Formulate appropriate dual problem.

A company produces 3 kinds of products A, B and C, which are sold for a price of 3, 7 and 5 Ls respectively, but their unit costs are 1, 3 and 2 Ls. Machine time and labour time are used in production process. For the product A 30 min of machine time and 50 min of labour time is needed. For the product B 50 min of machine time and 1.5 hours of labour time is needed. For the product C 40 min of machine time and 1 hour of labour time is needed. It is possible to use 25 hour of machine time and 40 hours of labour time per week. Exploitation instructions say that machines have to be used at least 10 hours per week.

The manager of the company wants to find out, how many of each product to produce, in order to obtain maximum profit.

Formulate a linear programming model formulate it in a basic standard or normal form and enhanced standard or canonical form. Formulate appropriate dual problem. A company produces 3 kinds of products - A, B and C, which are sold for a price of 3, 7 and 5 Ls respectively, but their unit costs are - 1, 3 and 2 Ls. Machine time and labour time are used in production process. For the product A 30 min of machine time and 50 min of labour time is needed. For the product B 50 min of machine time and 1.5 hours of labour time is needed. For the product C 40 min of machine time and 1 hour of labour time is needed. It is possible to use 25 hour of machine time and 40 hours of labour time per week. Exploitation instructions say that machines have to be used at least 10 hours per week. The manager of the company wants to find out, how many of each product to produce, in order to obtain maximum profit