Algebra

Linear Programming

Medium

applied

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function

$z = 1.50x + 1.00y$ ; the maximum value of $z$ will be:

52.5

61.3

72.4

✅ Correct Option: 2

In Linear Programming Problems, the maximum or minimum value of the objective function occurs at one of the corner points (vertices) of the feasible region.

From the shaded feasible region in the graph, the corner points are:

Point A: $(0, 0)$

Point B: $(35, 0)$

Point C: $(25, 15)$

Point D: $(0, 25)$

Substituting each corner point into the objective function $z = 1.50x + 1.00y$ :

At point A $(0, 0)$ :

$z = 1.50(0) + 1.00(0)$

$z = 0$

At point B $(35, 0)$ :

$z = 1.50(35) + 1.00(0)$

$z = 52.5 + 0$

$z = 52.5$

At point C $(25, 15)$ :

$z = 1.50(25) + 1.00(15)$

$z = 37.5 + 15$

$z = 52.5$

At point D $(0, 25)$ :

$z = 1.50(0) + 1.00(25)$

$z = 0 + 25$

$z = 25$

Comparing all values:

$z$ at A $= 0$

$z$ at B $= 52.5$

$z$ at C $= 52.5$

$z$ at D $= 25$

Therefore, the maximum value of $z = 52.5$

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$2x + 4y \leq 8$ ,

$3x + y \leq 6$ ,

$-x - y \geq -4$ ,

$x \geq 0$ , $y \geq 0$ is:

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The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

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Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$ , which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

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The corner points of the feasible region of a LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). If the objective function is $z = 4x + 6y$ , then the sum of maximum and minimum value of z is equal to:

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function z=1.50x+1.00yz = 1.50x + 1.00yz=1.50x+1.00y; the maximum value of zzz will be:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function

$z = 1.50x + 1.00y$ ; the maximum value of $z$ will be: