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based on programing

 A factory operates on two types of machines

Machine A
Machine B
Maximum available
Floor space
Number of operators needed
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.                                                                         


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


Not sure what goes with what.

1 Answer by Expert Tutors

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Christopher W. | Chris's Math TutoringChris's Math Tutoring
4.4 4.4 (14 lesson ratings) (14)
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.