maths

# A manufacturer produces nuts and bolts. It takes hours of work on machine and hours on machine  to product a package of nuts. It takes hours on machine and hour on machine to produce a package of bolts. He earns a profit of Rs per package on nuts and Rs per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operates his machines for at the most hours a day? From the above as a linear programming problem and solve it graphically.

## Let x be the no. of nuts & y be the bolts.We have to maximize x & y if the factory worked at capacity of 12hours per day.Clearly, Since we have only 12 hours of machine, we will use the following constraints:-The profit of nuts is Rs.17.5 and bolts is Rs. 7 .We need to maximize We can see that the feasible region is bounded and in the first quadrant.On solving the equations, and , we get and .Therefore, feasible points are Values of z are()The maximum profit which is when packets each of nuts & bolts are produced.

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