Advertisements
Advertisements
प्रश्न
A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are ₹ 5 and ₹ 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.
Advertisements
उत्तर
(i) Variables: Let x1 and x2 denote the number of pens in type A and type B.
(ii) Objective function:
Profit on x1 pens in type A = 5x1
Profit on x2 pens in type B is 3x2
Total profit = 5x1 + 3x2
Let Z = 5x1 + 3x2, which is the objective function.
Since the B total profit is to be maximized, we have to maximize Z = 5x1 + 3x2
(iii) Constraints:
Raw materials required for each pen A is twice as that of pen B.
i.e., for pen A raw material required is 2x1 and for B is x2.
Raw material is sufficient only for 1000 pens per day
∴ 2x1 + x2 ≤ 1000
Pen A requires 400 clips per day
∴ x1 ≤ 400
Pen B requires 700 clips per day
∴ x2 ≤ 700
(iv) Non-negative restriction:
Since the number of pens is non-negative, we have x1 > 0, x2 > 0.
Thus, the mathematical formulation of the LPP is Maximize Z = 5x1 + 3x2
Subject to the constrains
2x1 + x2 ≤ 1000, x1 ≤ 400, x2 ≤ 700, x1, x2 ≥ 0
APPEARS IN
संबंधित प्रश्न
In a cattle breading firm, it is prescribed that the food ration for one animal must contain 14. 22 and 1 units of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit of these two contains the following amounts of these three nutrients:
| Fodder → | Fodder 1 | Fodder 2 |
| Nutrient ↓ | ||
| Nutrients A | 2 | 1 |
| Nutrients B | 2 | 3 |
| Nutrients C | 1 | 1 |
The cost of fodder 1 is ₹ 3 per unit and that of fodder 2 ₹ 2. Formulate the LPP to minimize the cost.
Solve the following LPP by graphical method:
Maximize z = 11x + 8y, subject to x ≤ 4, y ≤ 6, x + y ≤ 6, 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 ______.
Choose the correct alternative :
Of all the points of the feasible region the optimal value of z is obtained at a point
Choose the correct alternative :
The half plane represented by 3x + 2y ≤ 0 constraints the point.
Fill in the blank :
“A gorage employs eight men to work in its shownroom and repair shop. The constraints that there must be at least 3 men in showroom and at least 2 men in repair shop are ______ and _______ respectively.
State whether the following is True or False :
Saina wants to invest at most ₹ 24000 in bonds and fixed deposits. Mathematically this constraints is written as x + y ≤ 24000 where x is investment in bond and y is in fixed deposits.
Solve the following linear programming problem graphically.
Maximize Z = 60x1 + 15x2 subject to the constraints: x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1, x2 ≥ 0.
The point which provides the solution of the linear programming problem, Max.(45x + 55y) subject to constraints x, y ≥ 0, 6x + 4y ≤ 120, 3x + 10y ≤ 180, is ______
The set of feasible solutions of LPP is a ______.
