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GUJCET 2025 Math Paper

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Question : 5 of 40

Marks: +1, -0

The coordinates of the corner points of the bounded feasible region are

(0, 0), (0, 40), (20, 40), (60, 20), (60, 0)

. The maximum of the objective function

z = 40x + 30y

is . . . . . . .

$2000$
$3400$
$2400$
$3000$

Solution:

Concept:

For a linear objective function over a bounded feasible region, the maximum value occurs at a corner point.

Explanation:

Given objective function:

z = 40x + 30y

Evaluate it at each corner point.

At

(0,0)

:

z = 40(0) + 30(0) = 0

.

At

(0,40)

:

z = 40(0) + 30(40) = 1200

.

At

(20,40)

:

z = 40(20) + 30(40) = 800 + 1200 = 2000

.

At

(60,20)

:

z = 40(60) + 30(20) = 2400 + 600 = 3000

.

At

(60,0)

:

z = 40(60) + 30(0) = 2400

.

The largest value among these is

3000

.

Answer:

The maximum value of

z = 40x + 30y

is

3000

.

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