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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Linear Programming

BITSAT 2020 · Mathematics · Linear Programming

The maximum value of z=6 x+8 y subject to constraints 2 x+y ≤ 30,...

The maximum value of z=6x+8yz=6 x+8 y subject to constraints 2x+y≤30,x+2y≤242 x+y \leq 30, x+2 y \leq 24 and x≥0,y≥0x \geq 0, y \geq 0 isThe maximum value of z=6 x+8 y subject to constraints 2 x+y ≤ 30, x+2 y ≤ 24 and x ≥ 0, y ≥ 0 is

Options

  1. A90
  2. B120
  3. C96
  4. D240

Correct answer

B. 120

Step-by-step solution

Here, 2x+y≤30,x+2y≤24,x,y≥02 x+y \leq 30, x+2 y \leq 24, x, y \geq 0 The shaded region represents the feasible region, hence z=6x+8y\mathrm{z}=6 \mathrm{x}+8 \mathrm{y}. Obviously it is maximum at (12,6) Hence z=12×6+8×6=120z=12 \times 6+8 \times 6=120 The maximum value of z=6 x+8 y subject to constraints 2 x+y ≤ 30, x+2 y ≤ 24 and x ≥ 0, y ≥ 0 is
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