10.In Fig. 12.11, the feasible region (shaded) for a LPP is shown. Determine themaximum and minimum value of Z = x+ 211.A manufacturer of electronic circuits has a stock of 200 resistors, 120 transistorsand 150 capacitors and is required to produce two types of circuits A and B.Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit isRs 50 and that on type B circuit is Rs 60, formulate this problem as a LPP sothat the manufacturer can maximise his profit.12.A firm has to transport 1200 packages using large vans which can carry 200packages each and small vans which can take 80 packages each. The cost forengaging each large van is Rs 400 and each small van is Rs 200. Not morethan Rs 3000 is to be spent on the job and the number of large vans can notexceed the number of small vans. Formulate this problem as a LPP given thatthe objective is to minimise cost.13.A company manufactures two types of screws A and B. All the screws have topass through a threading machine and a slotting machine. A box of Type Ascrews requires 2 minutes on the threading machine and 3 minutes on theslotting machine. A box of type B screws requires 8 minutes of threading onthe threading machine and 2 minutes on the slotting machine. In a week, eachmachine is available for 60 hours.y

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LINEAR PROGRAMMING 253On selling these screws, the company gets a profit of Rs 100 per box on typeA screws and Rs 170 per box on type B screws.Formulate this problem as a LPP given that the objective is to maximise profit.14.A company manufactures two types of sweaters : type A and type B. It costsRs 360 to make a type A sweater and Rs 120 to make a type B sweater. Thecompany can make at most 300 sweaters and spend at most Rs 72000 a day.The number of sweaters of type B cannot exceed the number of sweaters oftype A by more than 100. The company makes a profit of Rs 200 for eachsweater of type A and Rs 120 for every sweater of type B.Formulate this problem as a LPP to maximise the profit to the company.15.A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol costincreases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and onehour’s time. He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.Long Answer (L.A.)16.Refer to Exercise 11. How many of circuits of Type A and of Type B, shouldbe produced by the manufacturer so as to maximise his profit? Determine themaximum profit.17.Refer to Exercise 12. What will be the minimum cost?18.Refer to Exercise 13. Solve the linear programming problem and determinethe maximum profit to the manufacturer.19.Refer to Exercise 14. How many sweaters of each type should the companymake in a day to get a maximum profit? What is the maximum profit.20.Refer to Exercise 15. Determine the maximum distance that the man can travel.21.Maximise Z = x+ ysubject to x+ 4y≤8, 2x+ 3y≤12, 3x+ y≤9, x≥0, y≥