Chapter 12: Linear Programming

Important Questions

1. A small firm manufactures necklace and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes 1 hour to make a bracelet and half an hour make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs100 and that on a bracelet is Rs300, formulate an L.P.P for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

2. A cooperative society of farmers has 50 hectares of land to grow two crops A and B The profit from crops A and B per hectare are estimated as Rs. 10,500 B and Rs. 9,000 respectively. To control weeds a liquid herbicide has to be used for crops A and B at the rate of 20 litres and 10 litres per hectare, respectively. Further not more that 800 litres of herbicide should be used in order to protect fish and wildlife is more important drainage from this land. Keeping in mind that the protection of fish and other wildlife is more important than earing profit ,how much land should be allocated to each crop so as to maximize the total profit ? From an LPP from the above and solve it graphically.

3. A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine, Each unit of product A is sold at Rs. 7 profit and that of B at a profit of Rs 4. Find the production level per day for maximum profit graphically.

4. A factory makes tennis rackets and cricket bats. A tennis racket 1.5 hours of machine time and 3 hours of craftsman 's time in its making while a cricket bat takes 3 hours of machine time and 1 hours of craftsman's time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman's time. If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, find the number of tennis rackets and cricket bats that the factory must manufacture to earn the maximum profit. Make it as an L.P.P and solve it graphically.

5. A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of 70 paise and screws B at a profit of Rs1. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Formulate the above LPP and solve it graphically and find the maximum profit.

Sample Questions

1. A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs.100 and Rs.120 per unit respectively, how should he use his resource to maximize the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at same rate?

2. The postmaster of a local post office wishes to hire extra helpers during the Deepawali season, because of a large increase in the volume of mail handling and delivery. Because of the limited office space and the budgetary conditions, the number of temporary helpers must not exceed 10. According to past experience, a man can handle 300 letters and 80 packages per day, on the average, and a woman can handle 400 letters and 50 packets per day. The postmaster believes that the daily volume of extra mail and packages will be no less than 3400 and 680 respectively. A man receives Rs.225 a day and a woman receives Rs. 200 a day. How many men and women helpers should be hired to keep the pay-roll at a minimum? Formulate an LPP and solve it graphically.