A company manufacture two types of toys A and B. type A requires 5 minutes each for cutting and 10 minutes for each assembling. Type B requires 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours available for cutting and 4 hours available for assembling in a day. He earns a profit of ₹50 each on type A and ₹60 each on type B. How many toys of each type should the company manufacture in a day to maximize the profit?
Let the company manufacture x and y numbers of toys A and B.
∴According to the question,
5X + 8y
Maximize Z = 50x + 60y
The feasible region determined 5X + 8y is given by
The corner points of feasible region are A(0,0) , B(0,22.5) , C(12,15) , D(24,0).The value of Z at corner point is
The maximum value of Z is1500 and occurs at point (12,15).
The company should manufacture 12 A toys and 15 B toys to earn profit of rupees 1500.
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