Question

The given graph represents a feasible region. Minimum value of z=5x+4y is....,Select Proper option from the given options.
(a) 150
(b) 145
(c) 160
(d) 250

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The given graph represents a feasible region. Minimum value of z = 5x + 4y

(a) 150

(b) 145

(c) 160

(d) 250

EVALUATION

Here the given function to be minimized is

Min z = 5x + 4y

From the given figure we see that the corner points are (0 , 40) , (5 , 30) , (20 , 15) , (50 , 0)

Now we find the value of z at the corner points

$\sf{z_{(0 , 40)} = (5 \times 0) + (4 \times 40) = 0 + 160 = 160 }$

$\sf{z_{(5 , 30)} = (5 \times 5) + (4 \times 30) = 25 + 120 = 145 }$

$\sf{z_{(20 , 15)} = (5 \times 20) + (4 \times 15) = 100 + 60 = 160 }$

$\sf{z_{(50 , 0)} = (5 \times 50) + (4 \times 0) = 250 + 0 = 250 }$

Thus minimum value of z occurs at (5 , 30)

Also

$\sf{ z_{min} = 145}$

FINAL ANSWER

Hence the correct option is (b) 145

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