Q. The maximum value of $\mu = 3x + 4y , $ subject to the condition $x + y \leq 40 , x + 2y \leq 60 , x , y \geq 0$ is
Linear Programming
Solution:
Given, $P= 3x + 4y $
This graph has been draw from given constraints and maximum value of P will be at A or B or C .
$P_A = P_{(0 ,30)} = 3\times 0 + 4 \times 30 = 120 $
$P_B = P_{(20 ,20)} = 3\times 20 + 4 \times 20 = 140 $
$P_C = P_{(40 ,0)} = 3\times 40 + 0 = 120 $
Therefore $P_{max} = 140$
