GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

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Question : 52 of 65

Marks: +1, -0

The problem of maximizing

z=x_{1}-x_{2}

subject to constraints

x_{1}+x_{2} ≤ 10, x_{1} ≥ 0, x_{2} ≥ 0

and

x_{2} ≤ 5

has

no solution
one solution
two solution
more than two solutions

Solution:

Max.,

Z=x_{1}-x_{2}

Constratins :

x_{1}+x_{2} ≤ 10

x_{1} ≥ 0 ; x_{2} ≥ 0

and

x_{2} ≤ 5

Z(0,5)=0-5=-5

Z(5,5)=5-5=0

Z(10,0)=10-0=10

Z_{\max }=10

at

(10,0)

The problem has one solution

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