based on programing

Question

 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.      

Answer 1

Well for the first equation we know that we only have 18 units of floor space so the number of the 2 types of machines added together must be equal to or less than the max floor space 18,  or 2X + 3Y ≤ 18 

 

We do the same for the maximum number of operators or 4X + 3Y ≤ 24 

 

Solve for Y for each equation and graph them, where the two lines intersect each other should be the answer as long as Y > X which was the first stipulation.

 

Then plug in X and Y into the profit equation which is 400X + 600Y = P

 

I hope I didn't confuse you more.