The maximum value of Z=x+3y subject to the co | vedclass

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(D) The feasible region is determined by the constraints $2x+y \leq 20$,$x+2y \leq 20$,$x \geq 0$,and $y \geq 0$. The corner points of the feasible re

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$30$

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(D) The feasible region is determined by the constraints $2x+y \leq 20$,$x+2y \leq 20$,$x \geq 0$,and $y \geq 0$. The corner points of the feasible region are $O(0,0)$,$A(10,0)$,$B(\frac{20}{3}, \frac{20}{3})$,and $C(0,10)$. We evaluate $Z = x+3y$ at each corner point: At $O(0,0)$,$Z = 0 + 3(0) = 0$. At $A(10,0)$,$Z = 10 + 3(0) = 10$. At $B(\frac{20}{3}, \frac{20}{3})$,$Z = \frac{20}{3} + 3(\frac{20}{3}) = \frac{20}{3} + 20 = \frac{80}{3} \approx 26.67$. At $C(0,10)$,$Z = 0 + 3(10) = 30$. Comparing these values,the maximum value of $Z$ is $30$ at point $C(0,10)$.

The maximum value of $Z=x+3y$ subject to the constraints $2x+y \leq 20$,$x+2y \leq 20$,$x \geq 0$,$y \geq 0$ is:

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