मराठी

The Solution Set of the Inequation 2x + Y > 5 is (A) Half Plane that Contains the Origin (B) Open Half Plane Not Containing the Origin (C) Whole Xy-plane Except the Points Lying on the Line 2x + Y = 5 - Mathematics

Advertisements
Advertisements

प्रश्न

The solution set of the inequation 2x + y > 5 is

पर्याय

  •  half plane that contains the origin

  • open half plane not containing the origin

  • whole xy-plane except the points lying on the line 2x + y = 5

  • none of these

     
MCQ
Advertisements

उत्तर

 open half plane not containing the origin

On putting x = 0, y = 0 in the given inequality, we get
0 > 5, which is absurd.

Therefore, the solution set of the given inequality does not include the origin.

Thus, the solution set of the given inequality consists of the open half plane not containing the origin .

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 30: Linear programming - MCQ [पृष्ठ ६७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 30 Linear programming
MCQ | Q 1 | पृष्ठ ६७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A firm manufactures two types of products A and B and sells them at a profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2. Type A requires one minute of processing time on M1 and two minutes of M2; type B requires one minute on M1 and one minute on M2. The machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP.


A rubber company is engaged in producing three types of tyres AB and C. Each type requires processing in two plants, Plant I and Plant II. The capacities of the two plants, in number of tyres per day, are as follows:

Plant A B C
I 50 100 100
II 60 60 200

The monthly demand for tyre AB and C is 2500, 3000 and 7000 respectively. If plant I costs Rs 2500 per day, and plant II costs Rs 3500 per day to operate, how many days should each be run per month to minimize cost while meeting the demand? Formulate the problem as LPP.


A manufacturer can produce two products, A and B, during a given time period. Each of these products requires four different manufacturing operations: grinding, turning, assembling and testing. The manufacturing requirements in hours per unit of products A and B are given below.

  A B
Grinding 1 2
Turning 3 1
Assembling 6 3
Testing 5 4


The available capacities of these operations in hours for the given time period are: grinding 30; turning 60, assembling 200; testing 200. The contribution to profit is Rs 20 for each unit of A and Rs 30 for each unit of B. The firm can sell all that it produces at the prevailing market price. Determine the optimum amount of A and B to produce during the given time period. Formulate this as a LPP.


An automobile manufacturer makes automobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation, must work 5 man-days on each truck but only 2 man-days on each automobile. Shop B, which performs finishing operations, must work 3 man-days for each automobile or truck that it produces. Because of men and machine limitations, shop A has 180 man-days per week available while shop B has 135 man-days per week. If the manufacturer makes a profit of Rs 30000 on each truck and Rs 2000 on each automobile, how many of each should he produce to maximize his profit? Formulate this as a LPP.


A firm has to transport at least 1200 packages daily using large vans which carry 200 packages each and small vans which can take 80 packages each. The cost of engaging each large van is ₹400 and each small van is ₹200. Not more than ₹3000 is to be spent daily on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimize cost


Which of the following sets are convex?


Let X1 and X2 are optimal solutions of a LPP, then


The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y ≤ 18, x + y ≥ 10 ; xy ≥ 0 is


Consider a LPP given by
Minimum Z = 6x + 10y
Subjected to x ≥ 6; y ≥ 2; 2x + y ≥ 10; xy ≥ 0
Redundant constraints in this LPP are 


The objective function Z = 4x + 3y can be maximised subjected to the constraints 3x + 4y ≤ 24, 8x + 6y ≤ 48, x ≤ 5, y ≤ 6; xy ≥ 0


If the constraints in a linear programming problem are changed


Which of the following is not a convex set?


A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toys in a day. The profit is ₹ 50 each on a toy of type A and ₹ 60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution. 


The optimum value of the objective function of LPP occurs at the center of the feasible region.


Choose the correct alternative:

How does a constraint, “A washing machine can hold up to 8 kilograms of cloths (X)” can be given?


State whether the following statement is True or False:

The half-plane represented by 3x + 4y ≥ 12 includes the point (4, 3)


Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______


Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______


Determine the maximum value of Z = 4x + 3y if the feasible region for an LPP is shown in figure


Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0


Minimise Z = 3x + 5y subject to the constraints:
x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0


Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the point ______.


The common region determined by all the linear constraints of a LPP is called the ______ region.


In maximization problem, optimal solution occurring at corner point yields the ____________.


Conditions under which the object function is to be maximum or minimum are called ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×