Advertisements
Advertisements
प्रश्न
The set of feasible solutions of LPP is a ______.
विकल्प
Concave set
Convex set
Null set
None of these
Advertisements
उत्तर
The set of feasible solutions of LPP is a convex set.
APPEARS IN
संबंधित प्रश्न
A company manufactures two types of chemicals Aand 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 and the total availability of P and Q.
| Chemical→ | A | B | Availability |
| Raw Material ↓ | |||
| 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. (Assume that the entire production of A and B can be sold). How many units of the chemicals A and B should be manufactured so that the company gets a maximum profit? Formulate the problem as LPP to maximize profit.
A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 in magazines A and B per copy. These are processed on three Machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II, and 2 hours on machine III. Magazine B requires 3 hours on machine I, 2 hours on machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, and 60 hours per week respectively. Formulate the LPP to determine weekly production of magazines A and B, so that the total profit is maximum.
Select the appropriate alternatives for each of the following question:
The value of objective function is maximum under linear constraints
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 ______.
If the corner points of the feasible solution are (0, 10), (2, 2) and (4, 0), then the point of minimum z = 3x + 2y is ______.
Solve each of the following inequations graphically using XY-plane:
4x - 18 ≥ 0
Solve each of the following inequations graphically using XY-plane:
5y - 12 ≥ 0
Solve the following LPP:
Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0.
Solve the following LPP:
Maximize z =60x + 50y subject to
x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0.
A company manufactures two types of fertilizers F1 and F2. Each type of fertilizer requires two raw materials A and B. The number of units of A and B required to manufacture one unit of fertilizer F1 and F2 and availability of the raw materials A and B per day are given in the table below:
| Raw Material\Fertilizers | F1 | F2 | Availability |
| A | 2 | 3 | 40 |
| B | 1 | 4 | 70 |
By selling one unit of F1 and one unit of F2, company gets a profit of ₹ 500 and ₹ 750 respectively. Formulate the problem as L.P.P. to maximize the profit.
Choose the correct alternative :
The corner points of the feasible region are (0, 0), (2, 0), `(12/7, 3/7)` and (0,1) then the point of maximum z = 7x + y
The optimal value of the objective function is attained at the ______ points of the feasible region.
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.
State whether the following is True or False :
The feasible solution of LPP belongs to only quadrant I.
Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points
Solve the following linear programming problems by graphical method.
Minimize Z = 3x1 + 2x2 subject to the constraints 5x1 + x2 ≥ 10; x1 + x2 ≥ 6; x1 + 4x2 ≥ 12 and x1, x2 ≥ 0.
Maximize: z = 3x1 + 4x2 subject to 2x1 + x2 ≤ 40, 2x1 + 5x2 ≤ 180, x1, x2 ≥ 0. In the LPP, which one of the following is feasible comer point?
Given an L.P.P maximize Z = 2x1 + 3x2 subject to the constrains x1 + x2 ≤ 1, 5x1 + 5x2 ≥ 0 and x1 ≥ 0, x2 ≥ 0 using graphical method, we observe
A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, While B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs 30 minutes while M2 is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.
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.
Solve the following linear programming problem graphically.
Maximize Z = 3x1 + 5x2 subject to the constraints: x1 + x2 ≤ 6, x1 ≤ 4; x2 ≤ 5, and x1, x2 ≥ 0.
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 maximum value of Z = 3x + 5y, subject to 3x + 2y ≤ 18, x ≤ a, y ≤ 6, x, y ≥ 0 is ______.
The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.
The optimal value of the objective function is attained at the ______ of feasible region.
Shamli wants to invest ₹ 50, 000 in saving certificates and PPF. She wants to invest atleast ₹ 15,000 in saving certificates and at least ₹ 20,000 in PPF. The rate of interest on saving certificates is 8% p.a. and that on PPF is 9% p.a. Formulation of the above problem as LPP to determine maximum yearly income, is ______.
For the following shaded region, the linear constraint are:
Solve the following LPP:
Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.
