Q. 55.0( 1 Vote )
A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.[CBSE 2011]
Let the merchant stock x number of desktop models and y number of portable models.
∴ x and y ≥ 0
According to the given condition
The cost of a desKtop model is Rs25000 and that of a portable model is Rs 40,000. The merchant can invest up to Rs 7000000
⇒ 25000x + 40000y ≤ 7000000
⇒ 5x + 8y ≤ 1400
The monthly demand of computers will not exceed 250 units.
⇒ x+ y ≤ 250
The profit on a desktop model is Rs 4500 and the profit on a portable model is Rs5000.
Total profit , Z = 4500x + 5000y
Thus the mathematical formulation of the data is
Maximize Z = 4500x + 5000y
Subject to constraints
5x + 8y ≤ 1400
x+ y ≤ 250
x and y ≥ 0
the feasible region by the system of constraints is as follows:
The cornet points are A(250,0) , B( 200,50) and C(0 ,175)
The value of Z at the given corners points are:
The maximum value of Z is Rs1150000 at ( 200,50)
Thus the merchant should stock 200 desktop models and 50 portable models to earn the maximum profit of Rs 11, 50, 000.
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