Algebra

Linear Programming

Medium

core

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$ , $(0, 40)$ , $(20, 40)$ , $(60, 20)$ , $(60, 0)$ . If the objective function is $z = 4x + 3y$ , then which one of the following is true?

Max $z > 400$

Max $z < 400$

Max $z = 400$

Max $z = 350$

✅ Correct Option: 2

The corner points of the feasible region are $(0, 0)$ , $(0, 40)$ , $(20, 40)$ , $(60, 20)$ , $(60, 0)$ .

The objective function is $z = 4x + 3y$ .

In linear programming, the maximum or minimum value of the objective function occurs at one of the corner points of the feasible region.

At point $(0, 0)$ :

$z = 4(0) + 3(0)$

$z = 0$

At point $(0, 40)$ :

$z = 4(0) + 3(40)$

$z = 0 + 120$

$z = 120$

At point $(20, 40)$ :

$z = 4(20) + 3(40)$

$z = 80 + 120$

$z = 200$

At point $(60, 20)$ :

$z = 4(60) + 3(20)$

$z = 240 + 60$

$z = 300$

At point $(60, 0)$ :

$z = 4(60) + 3(0)$

$z = 240 + 0$

$z = 240$

Comparing all values:

At $(0, 0)$ : $z = 0$

At $(0, 40)$ : $z = 120$

At $(20, 40)$ : $z = 200$

At $(60, 20)$ : $z = 300$

At $(60, 0)$ : $z = 240$

The maximum value of $z = 300$ occurs at point $(60, 20)$ .

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The corner points of the feasible region determined by a system of linear constraints are (0,0)(0, 0)(0,0), (0,40)(0, 40)(0,40), (20,40)(20, 40)(20,40), (60,20)(60, 20)(60,20), (60,0)(60, 0)(60,0). If the objective function is z=4x+3yz = 4x + 3yz=4x+3y, then which one of the following is true?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$ , $(0, 40)$ , $(20, 40)$ , $(60, 20)$ , $(60, 0)$ . If the objective function is $z = 4x + 3y$ , then which one of the following is true?