Algebra

Linear Programming

Medium

applied

As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is

$\frac{3}{2}$

✅ Correct Option: 3

The objective function is $z = 2x + y$ , which needs to be maximized over the shaded feasible region.

In Linear Programming, the maximum value of the objective function always occurs at one of the corner points of the feasible region.

From the graph, the vertices of the shaded feasible region are:

Point A: $(0, 0)$

Point B: $(5, 0)$

Point C: $(4, 2)$

Point D: $(0, 4)$

Evaluating the objective function $z = 2x + y$ at each corner point:

At point A $(0, 0)$ :

$z = 2(0) + 0$

$z = 0$

At point B $(5, 0)$ :

$z = 2(5) + 0$

$z = 10$

At point C $(4, 2)$ :

$z = 2(4) + 2$

$z = 8 + 2$

$z = 10$

At point D $(0, 4)$ :

$z = 2(0) + 4$

$z = 4$

Comparing the values: $0, 10, 10, 4$

The maximum value of $z$ is $10$ , which occurs at points B $(5, 0)$ and C $(4, 2)$ .

Therefore, the maximum value of the objective function is $10$ .

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As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function z=2x+yz = 2x + yz=2x+y is

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As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is