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BITSAT 2018

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

BITSAT 2018 · Mathematics · Linear Programming

The coordinates of the point at which minimum value of Z = 7x - 8y...

The coordinates of the point at which minimum value of

Z = 7x - 8y

subject to constraints

x + y - 20 \le 0, y \ge 5, x \ge 0, y \ge 0

& is attained, is The coordinates of the point at which minimum value of Z = 7x - 8y subject to constraints x + y - 20 ≤ 0, y ≥ 5, x ≥ 0,

The coordinates of the point at which minimum value of Z = 7x - 8y subject to constraints x + y - 20 ≤ 0, y ≥ 5, x ≥ 0,

Options

A $\left(20, 0\right)$
B $\left(15, 5\right)$
C $\left(0, 5\right)$
D $\left(0, 20\right)$

Correct answer

D. $\left(0, 20\right)$

Step-by-step solution

Feasible region is

ABCA and Z = 7x - 8y

The coordinates of the point at which minimum value of Z = 7x - 8y subject to constraints x + y - 20 ≤ 0, y ≥ 5, x ≥ 0,

At $A\left(0, 5\right), Z = 7 \times 0 - 8 \times 5 = - 40$

At $B\left(15, 5\right), Z = 7\left(15\right) - 8\left(5\right) = 65$

At $C\left(0, 20\right), Z = 7\left(0\right) - 8 \left(20\right) = - 160$

Hence, the minimum value of $Z$ is attained at point \left(0, 20\right) $</p><p>So, option \left(d\right)$ is correct.

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