Linear Programming [Word Problems]

Linear Programming Practice Questions

  1. A manufacturer produces two types of steel trunks. He has two machines A and B. The first type of trunk requires 3 hours on machine A and 3 hours on machine B. The second type requires 3 hours on machine A and 2 hours on machine B. Machine A and B work at most for 18 hours per day respectively. He earns a profit of Rs.30 and Rs.25 per trunk of the first type and second type must he make each day to make the maximum profit?
  2. A company manufactures two types of toys A and B. Type A requires 5 minutes each for cutting and 10 minutes each for assembling. Type B requires 8 minutes each for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling in a day. The profit is Rs.50 on type A and Rs.60 on type B. How many toys of each type should the company manufactures in a day to maximise profit.
  3. A diet for a side person must contain at least 4000 vitamins, 50 units of minerals and 1400 calories. Two foods A and B are available at a cost of Rs.4 and Rs.3 per unit respectively. If one unit of A contains 200 units of vitamins, 1 unit of minerals and 40 units of calories, one unit of B contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of foods should be used to have the least cost.
  4. Custom cars does van conversions. The custom conversion requires 15 hours of shop time, 8 hours of painting time, and 1 hour of inspection time. The deluxe conversion requires 12 hrs of shop time, 12 hrs of painting time and 1.5 hrs if inspection time. There are 90 hours of shop time, 72 hrs of painting and 10 hrs of inspection time available during the coming two weeks. How many conversions of each type should custom Cars perform assuming that each custom conversions results in Rs.175 profit and each deluxe conversion results in Rs.225 profit. Find maximum profit.
  5. A manufacturer produces two types of soap bars using two machines A and B. A is operated for 2 minutes and B for 3 minutes to manufacture the first type, while it takes 3 minutes on machine A and 5 minutes on machine to manufacture the second type. Each machine can be operated at the most for 8 hours per day. The two types of soap bars are sold at a profit of Rs.0.25 and Rs.0.50 each. Assuming that the manufacturer can sell all bars of soap of each type should be manufactured per day so as to maximise his profit.
  6. A resourceful home decorator manufactures two types of lamps say A and B. Both lamps go through two technicians, first a cutter, second a finisher. Lamp A requires 2 hours of finishers time. The cutter has 104 hours and finisher has 76 hours of time available each month. Profit on one lamp A is Rs.6 and on one lamp B Rs.11. Assuming that he can sell all that he can sell all that he produces, how many of each type of lamps should he manufacture to obtain the best return.
  7. A factory  produces two products A and B. Each of the product A requires 2 hours of mounding, 3 hours of grinding and 4 hours of polishing and each of product B requires 4 hours of moulding, 2 hours of grinding and 2 hours of polishing. The factory has moulding machine available for 20 hours, grinding machine for 24 hours and polishing machine available for 13 hours. The profit is Rs.5 per unit of And Rs.3 per unit of B and the factory can sell all that it produces. Formulate the problem as a linear programming problem to maximise the profit. 

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