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 = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.
The point of which the maximum value of x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x, ≥ 0, y ≥ 0 is is obtained at ______.
The corner points of the feasible solution are (0, 0), (2, 0), `(12/7, 3/7)`, (0, 1). Then z = 7x + y is maximum at ______.
A company produces mixers and food processors. Profit on selling one mixer and one food processor is Rs 2,000 and Rs 3,000 respectively. Both the products are processed through three machines A, B, C. The time required in hours for each product and total time available in hours per week on each machine arc as follows:
| Machine | Mixer | Food Processor | Available time |
| A | 3 | 3 | 36 |
| B | 5 | 2 | 50 |
| C | 2 | 6 | 60 |
How many mixers and food processors should be produced in order to maximize the profit?
The feasible region is the set of point which satisfy.
Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
x − y ≤ 1, x − y ≥ 0, x ≥ 0, y ≥ 0 are the constant for the objective function z = x + y. It is solvable for finding optimum value of z? Justify?
The values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______
Food F1 contains 2, 6, 1 units and food F2 contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F1 is Rs. 85 and food F2 is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.
