1. Tardigrade
  2. Question
  3. Mathematics
  4. The maximum value of P = 6x + 8y subject to constraints 2x + y ≤ 30 , x + 2y ≤ 24 and x ≥ 0 , y ≥ 0 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The maximum value of $P = 6x + 8y$ subject to constraints $2x + y \leq 30 , x + 2y \leq 24$ and $ x \geq 0 , y \geq 0 $ is

Linear Programming

Solution:

Here , $2x + y \leq 30, x + 2y \leq 24 , x , y \geq 0 $
The shaded region represents the feasible region, hence $P = 6x + 8y$. Obviously it is maximum at (12, 6).
Hence, $P = 12 \times 6 + 8 \times 6 = 120 $

Solution Image