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State whether the following statement is True or False: The point (6, 4) does not belong to the feasible region bounded by 8x + 5y ≤ 60, 4x + 5y ≤ 40, 0 ≤ x, y - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

The point (6, 4) does not belong to the feasible region bounded by 8x + 5y ≤ 60, 4x + 5y ≤ 40, 0 ≤ x, y

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

True

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Linear Programming - Q.2 (B)

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Inequations Equations X intercept Y intercept Region
5x + y ≥ 10 5x + y = 10 ( ___, 0) (0, 10) Away from origin
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x + 4y ≥ 12 x + 4y = 12 (12, 0) (0, 3) Away from origin
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∵ Origin has not satisfied the inequations.

∴ Solution of the inequations is away from origin.

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In the figure, ABCD represents

The set of the feasible solution where

A(12, 0), B( ___, ___ ), C ( ___, ___ ) and D(0, 10).

The coordinates of B are obtained by solving equations

x + 4y = 12 and x + y = 6

The coordinates of C are obtained by solving equations

5x + y = 10 and x + y = 6

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Point Coordinates Z = 4x + 5y Values Remark
A (12, 0) 4(12) + 5(0) 48  
B ( ___, ___ ) 4( ___) + 5(___ ) ______ ______
C ( ___, ___ ) 4( ___) + 5(___ ) ______  
D (0, 10) 4(0) + 5(10) 50  

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