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BITSAT 2018

Exam: BITSAT
Year: 2018
Subject: Mathematics
Chapter: Linear Programming

BITSAT 2018 · Mathematics · Linear Programming

The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤...

The maximum value of

Z = 4x + 2y

subject to constraints

2x + 3y \le 18, x + y \ge 10

and

x, y \ge 0

& is

The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10 and x, y ≥ 0 & is

Options

A $20$
B $36$
C $40$
DNone of these

Correct answer

D. None of these

Step-by-step solution

We have,

$Z = 4x + 2y$

And,

$2x + 3y \le 18, x + y \ge 10$

Let

${L}_{1}: 2x + 3y = 18$

${L}_{2}: x + y = 10$

${L}_{3}: x = 0$

${L}_{4}: y = 0$

Then the feasible region is

The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10 and x, y ≥ 0 & is

From the figure, it is clear that there is no common area. So, we cannot find maximum value of~ $Z$ .

Hence, option $\left(d\right)$ is correct.

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