Q. 165.0( 1 Vote )
A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand – operated. It takes 4 minutes on the automatic and 6 minutes on the hand operated machines to manufacture a packet of screws ‘B’. Each machine is availble for at most 4 hours on any day. The manufacturer can sell a packet of screws ‘A’ at a profit of 70 paise and screws ‘B’ at a profit of Rs. 1. Assuming that he can sell all the screws he manufactrures, how many packets 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.[CBSE 2018]
Let the factory manufactures x screws of type A and y screws of type B on each day.
∴ x≥0, y≥0
The constraints are
4x + 6y ≤ 240
6x + 3y ≤ 240
Total profit: Z = 0.70x + y
2x + 3y ≤ 120
2x + y ≤ 120
Now, plotting the equations 2x + 3y ≤ 120 and 2x + y ≤ 120 we get,
∴ the common feasible region is OCBAO.
The maximum value of ‘Z’ is 41 at (30,20). Thus the factory showed produce 30 packages at screw A and 20 packages of screw B to get the maximum profit of Rs.41.
Rate this question :
A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of the first machine is 12 hours and that of the 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 the first machine and 1 hour on the second machine. Each unit of product A is sold at ` 7 profit and that of B at a profit of ` 4. Find the production level per day for maximum profit graphically.Mathematics - Board Papers
A retired person wants to invest an amount of ₹ 50,000. His broker recommends investing in two types of bonds ‘A’ and ‘B’ yielding 10% and 9% return respectively on the invested amount. He decides to invest at least ₹ 20,000 in bond ‘A’ and at least ₹ 10,000 in bond ‘B’. He also wants to invest at least as much in bond ‘A’ as in bond ‘B’. Solve this linear programming problem graphically to maximize his returns.Mathematics - Board Papers
A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs80 on each piece of type A, and Rs120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?Mathematics - Board Papers