A factory operates on two types of machines

Machine A

Machine B

Maximum available

Floor space

2

3

18

Number of operators needed

4

3

24

There are more machines of type B than those of type A. Taking the number of machines of type A used as X and that of types B as Y, form the inequalities in X and Y. If the profit from using machine A is sh. 400 per hour and that from using machine B is sh. 600 per hour. Find graphically, the number of machines of each type that should be in use to give maximum profit per hour hence find the maximum profit.

Required

Develop a linear program and hence find the optimal solution for the problem.

Machine A

Machine B

Maximum available

Floor space

2

3

18

Number of operators needed

4

3

24

There are more machines of type B than those of type A. Taking the number of machines of type A used as X and that of types B as Y, form the inequalities in X and Y. If the profit from using machine A is sh. 400 per hour and that from using machine B is sh. 600 per hour. Find graphically, the number of machines of each type that should be in use to give maximum profit per hour hence find the maximum profit.

Required

Develop a linear program and hence find the optimal solution for the problem.

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