Advertisements
Advertisements
प्रश्न
Objective function of LPP is ______.
पर्याय
A constraint
A function to be maximised or minimised
A relation between the decision variables
A feasible region
Equation of straight line
Advertisements
उत्तर
Objective function of LPP is a function to be maximised or minimised.
APPEARS IN
संबंधित प्रश्न
Which of the following statements is correct?
Find the feasible solution of the following inequation:
2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0
Find the feasible solution of the following inequation:
x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.
Find the feasible solution of the following inequations:
x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0
A company produces two types of articles A and B which requires silver and gold. Each unit of A requires 3 gm of silver and 1 gm of gold, while each unit of B requires 2 gm of silver and 2 gm of gold. The company has 6 gm of silver and 4 gm of gold. Construct the inequations and find feasible solution graphically.
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.
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.
A doctor has prescribed two different units of foods A and B to form a weekly diet for a sick person. The minimum requirements of fats, carbohydrates and proteins are 18, 28, 14 units respectively. One unit of food A has 4 units of fat, 14 units of carbohydrates and 8 units of protein. One unit of food B has 6 units of fat, 12 units of carbohydrates and 8 units of protein. The price of food A is ₹ 4.5 per unit and that of food B is ₹ 3.5 per unit. Form the LPP, so that the sick person’s diet meets the requirements at a minimum cost.
Solve the following L.P.P. by graphical method:
Minimize: z = 8x + 10y
Subject to: 2x + y ≥ 7, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0.
Which of the following is correct?
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 ______.
Solution of LPP to minimize z = 2x + 3y, such that x ≥ 0, y ≥ 0, 1 ≤ x + 2y ≤ 10 is ______.
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 ______.
The half-plane represented by 3x + 2y < 8 contains the point ______.
Solve the following LPP:
Maximize z = 4x + 2y subject to 3x + y ≤ 27, x + y ≤ 21, x ≥ 0, y ≥ 0.
Sketch the graph of the following inequation in XOY co-ordinate system:
|x + 5| ≤ y
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.
Solve the following LPP:
Minimize z = 4x + 2y
Subject to 3x + y ≥ 27, x + y ≥ 21, x + 2y ≥ 30, x ≥ 0, y ≥ 0
A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:
| Product → | Chair (x) | Table (y) | Available time (hours) |
| Machine ↓ | |||
| Assembling | 3 | 3 | 36 |
| Finishing | 5 | 2 | 50 |
| Polishing | 2 | 6 | 60 |
Formulate the above problem as LPP. Solve it graphically
A chemical company produces a chemical containing three basic elements A, B, C, so that it has at least 16 litres of A, 24 litres of B and 18 litres of C. This chemical is made by mixing two compounds I and II. Each unit of compound I has 4 litres of A, 12 litres of B and 2 litres of C. Each unit of compound II has 2 litres of A, 2 litres of B and 6 litres of C. The cost per unit of compound I is ₹ 800 and that of compound II is ₹ 640. Formulate the problems as LPP and solve it to minimize the cost.
A firm manufactures two products A and B on which profit earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. The product A requires one minute of processing time on M1 and two minutes of processing time on M2, B requires one minute of processing time on M1 and one minute of processing time on M2. Machine M1 is available for use for 450 minutes while M2 is available for 600 minutes during any working day. Find the number of units of products A and B to be manufactured to get the maximum profit.
A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to machine shop for finishing. The number of man hours of labour required in each shop for production of A and B and the number of man hours available for the firm are as follows:
| Gadgets | Foundry | Machine Shop |
| A | 10 | 5 |
| B | 6 | 4 |
| Time available (hours) | 60 | 35 |
Profit on the sale of A is ₹ 30 and B is ₹ 20 per unit. Formulate the L.P.P. to have maximum profit.
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 printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 on 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, 60 hours per week respectively. Formulate the Linear programming problem to maximize the profit.
Solve the following L.P.P. by graphical method:
Maximize: Z = 4x + 6y
Subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.
Choose the correct alternative :
Feasible region; the set of points which satify.
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
If the corner points of the feasible region are (0, 0), (3, 0), (2, 1) and `(0, 7/3)` the maximum value of z = 4x + 5y is ______.
Choose the correct alternative :
The half plane represented by 3x + 2y ≤ 0 constraints the point.
Choose the correct alternative :
The half plane represented by 4x + 3y ≥ 14 contains the point
The optimal value of the objective function is attained at the ______ points of the feasible region.
The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at
Which value of x is in the solution set of inequality − 2X + Y ≥ 17
Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the Linear Programming problem graphically:
Maximize z = 3x + 5y subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0 also find the maximum value of z.
Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0.
Minimize z = 6x + 21y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points
Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≥ 6, y ≥ 0 is this LPP solvable? Justify your answer.
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?
State whether the following statement is True or False:
LPP is related to efficient use of limited resources
The variables involved in LPP are called ______
Constraints are always in the form of ______ or ______.
The constraint that in a particular XII class, number of boys (y) are less than number of girls (x) is given by ______
Solve the following linear programming problems by graphical method.
Maximize Z = 22x1 + 18x2 subject to constraints 960x1 + 640x2 ≤ 15360; x1 + x2 ≤ 20 and x1, x2 ≥ 0.
Solve the following linear programming problems by graphical method.
Minimize Z = 20x1 + 40x2 subject to the constraints 36x1 + 6x2 ≥ 108; 3x1 + 12x2 ≥ 36; 20x1 + 10x2 ≥ 100 and x1, x2 ≥ 0.
The maximum value of the objective function Z = 3x + 5y subject to the constraints x ≥ 0, y ≥ 0 and 2x + 5y ≤ 10 is:
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.
A firm manufactures pills in two sizes A and B. Size A contains 2 mgs of aspirin, 5 mgs of bicarbonate and 1 mg of codeine. Size B contains 1 mg. of aspirin, 8 mgs. of bicarbonate and 6 mgs. of codeine. It is found by users that it requires at least 12 mgs. of aspirin, 74 mgs. of bicarbonate and 24 mgs. of codeine for providing immediate relief. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LLP.
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.
Minimize Z = 200x1 + 500x2 subject to the constraints: x1 + 2x2 ≥ 10; 3x1 + 4x2 ≤ 24 and x1 ≥ 0, 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.
Which of the following can be considered as the objective function of a linear programming problem?
The minimum value of z = 5x + 13y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10, x ≥ 0, y ≥ 2 is ______
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 ______
Solution which satisfy all constraints is called ______ solution.
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 ______.
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.
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.
Find graphical solution for the following system of linear in equation:
x + 2y ≥ 4, 2x - y ≤ 6
