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Question

The coordinate of the point at which minimum value of z=7x-8y subject to constraints x+y-200,y5,x0,y0 is attained, is:


A

(20,0)

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B

(15,5)

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C

(0,5)

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D

(0,20)

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Solution

The correct option is D

(0,20)


Explanation for the correct option:

Finding minimum value of Z

Given objective function :

z=7x-8y

Subjected to,

x+y-200y5x0y0

Now consider these constrains like a equation and graphing it simultaneously

Linear Programming Problems JEE Questions Q26

Here, the corner points as 0,20, 0,5 and 15,5

Now checking the value of Z at every point

At 0,20Z=7×0-8×20=-160

At 0,5Z=7×0-8×5=-40

At 15,5Z=7×15-8×5=65

Thus, Z is minimum at 0,20

Hence, option (D) is the correct answer.


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