मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Objective function of LPP is ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Objective function of LPP is ______.

पर्याय

  • a constraint

  • a function to be maximized or minimized

  • a relation between the decision variables

  • equation of a straight line

MCQ
रिकाम्या जागा भरा

उत्तर

Objective function of LPP is a function to be maximized or minimized.

shaalaa.com
Linear Programming Problem (L.P.P.)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Linear Programming - Miscellaneous exercise 7 [पृष्ठ २४२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 7 Linear Programming
Miscellaneous exercise 7 | Q 3 | पृष्ठ २४२

संबंधित प्रश्‍न

Find the feasible solution of the following inequation:

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9,  x ≥ 0, y ≥ 0.


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 Machine 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. Formulate the LPP to maximize the profit, if he operates the machine M1, for almost 10 hours a day and machine M2 for almost 12 hours a day.


Solve the following LPP by graphical method:

Maximize z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.


Solve the following LPP by graphical method:

Minimize z = 8x + 10y, subject to 2x + y ≥ 7, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0.


The maximum value of z = 10x + 6y subject to the constraints 3x + y ≤ 12, 2x + 5y ≤ 34, x, ≥ 0, y ≥ 0 is ______.


Of all the points of the feasible region, the optimal value of z obtained at the point lies ______.


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, 0), (3, 0), (2, 1), `(0, 7/3)` the maximum value of z = 4x + 5y is ______.


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 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


Find graphical solution for the following system of linear in equation:

3x + 4y ≤ 12, x - 2y ≥ 2, y ≥ - 1


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 ₹ 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 product 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 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 :

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


Choose the correct alternative :

The half plane represented by 4x + 3y ≥ 14 contains the point


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.


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


Constraints are always in the form of ______ or ______.


A company manufactures two models of voltage stabilizers viz., ordinary and auto-cut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at the company’s own works. The assembly and testing time required for the two models are 0.8 hours each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests a maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at ₹ 100 and ₹ 150 respectively. Formulate the linear programming problem.


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.


In the given graph the coordinates of M1 are


The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is


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.


The values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______


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.


Solve the following LPP:

Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.


Sketch the graph of the following inequation in XOY co-ordinate system.

x + y ≤ 0


Find graphical solution for the following system of linear in equation:

x + 2y ≥ 4, 2x - y ≤ 6


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×