Advertisements
Advertisements
प्रश्न
A company produces two types of products say type A and B. Profits on the two types of product are ₹ 30/- and ₹ 40/- per kg respectively. The data on resources required and availability of resources are given below.
| Requirements | Capacity available per month | ||
| Product A | Product B | ||
| Raw material (kgs) | 60 | 120 | 12000 |
| Machining hours/piece | 8 | 5 | 600 |
| Assembling (man hours) | 3 | 4 | 500 |
Formulate this problem as a linear programming problem to maximize the profit.
Advertisements
उत्तर
(i) Variables: Let x1 and x2 denote the two types products A and B respectively.
(ii) Objective function:
Profit on x1 units of type A product = 30x1
Profit on x2 units of type B product = 40x2
Total profit = 30x1 + 40x2
Let Z = 30x1 + 40x2, which is the objective function.
Since the profit is to be maximized, we have to maximize Z = 30x1 + 40x2
(iii) Constraints:
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
(iv) Non-negative constraints: Since the number of products on type A and type B are non-negative, we have x1, x2 ≥ 0
Thus, the mathematical formulation of the LPP is Maximize Z = 30x1 + 40x2
Subject to the constraints,
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
x1, x2 ≥ 0
APPEARS IN
संबंधित प्रश्न
Solve the following LPP by graphical method:
Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.
The corner points of the feasible solution given by the inequation x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0 are ______.
Solve each of the following inequations graphically using XY-plane:
y ≤ - 3.5
A company manufactures two types of chemicals A and B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B.
| Raw Material \Chemical | A | B | Availability |
| p | 3 | 2 | 120 |
| Q | 2 | 5 | 160 |
The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. Formulate the problem as L.P.P. to maximize the profit.
A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M1 and M2. A package of bulbs requires 1 hour of work on Machine M1 and 3 hours of work on M2. A package of tubes requires 2 hours on Machine M1 and 4 hours on Machine M2. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12 hours, then formulate the L.P.P. to maximize the profit.
Which value of x is in the solution set of inequality − 2X + Y ≥ 17
Solve the following linear programming problem graphically.
Maximise Z = 4x1 + x2 subject to the constraints x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1 ≥ 0, x2 ≥ 0.
The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.
The maximum value of Z = 9x + 13y subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0 is ______.
Two kinds of foods A and B are being considered to form a weekly diet. The minimum weekly requirements of fats, Carbohydrates and proteins are 12, 16 and 15 units respectively. One kg of food A has 2, 8 and 5 units respectively of these ingredients and one kg of food B has 6, 2 and 3 units respectively. The price of food A is Rs. 4 per kg and that of food B is Rs. 3 per kg. Formulate the L.P.P. and find the minimum cost.
