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Question

# A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours of work on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts.Then number of packages that can be produced to maximize his profits, if he operates each machine for at most 12 hours a day, is

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Solution

## Let x,y packages of nuts and bolts respectively be produced. Now, maximum working hour of both machines is 12. For machine A:x+3y≤12⋯(i) For machine B:3x+y≤12⋯(ii) and x,y≥0⋯(iii) Objective function :Z=17.5x+7y Now, plotting the graph of given constraints : We get feasible region as OBEC. Now, value of objective function Z=17.5x+7y at corner points is tabulated below. Corner points : (x,y) Value : Z=17.5x+7y O(0,0) 0 B(0,4) 28 C(4,0) 70 E(3,3) 73.5 So, maximum profits can be made by producing 3 packages of nuts and 3 packages of bolts. ∴6 packages should be produced daily.

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