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Choose the correct alternative : The half plane represented by 4x + 3y ≥ 14 contains the point - Mathematics and Statistics

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प्रश्न

Choose the correct alternative :

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

पर्याय

  • (0, 0)

  • (2, 2)

  • (3, 4)

  • (1, 1)

MCQ
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उत्तर

Only (3, 4) satisfies the given inequality.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Linear Programming - Miscellaneous Exercise 6 [पृष्ठ १०३]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 6 Linear Programming
Miscellaneous Exercise 6 | Q 1.15 | पृष्ठ १०३

संबंधित प्रश्‍न

Which of the following statements is correct?


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2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0


Find the feasible solution of the following inequation:

3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 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.


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.


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Select the appropriate alternatives for each of the following question:

The value of objective function is maximum under linear constraints


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 ______.


The half-plane represented by 4x + 3y >14 contains the point ______.


Solve the following LPP:

Maximize z = 4x + 2y subject to 3x + y ≤ 27, x + y ≤ 21, x ≥ 0, y ≥ 0.


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- 11x - 55 ≤ 0


Solve each of the following inequations graphically using XY-plane:

5y - 12 ≥ 0


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3x + 4y ≤ 12, x - 2y ≥ 2, y ≥ - 1


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Maximize z =60x + 50y  subject to

x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0.


Choose the correct alternative :

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Choose the correct alternative :

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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


Choose the correct alternative:

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Subject to 3x + 2y ≤ 12,

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x ≥ 0,

y ≥ 0.


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

x + 2y ≥ 4, 2x - y ≤ 6


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