The maximum value of the objective function Z | vedclass

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(B) The feasible region is determined by the constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,and $y \geq 0$. The vertices of the feasible regi

Vedclass · Accepted Answer

$21$

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(B) The feasible region is determined by the constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,and $y \geq 0$. The vertices of the feasible region are $O(0, 0)$,$A(0, 16/3)$,$B(5, 2)$,and $C(7, 0)$.We evaluate the objective function $Z = 3x + 2y$ at each vertex:At $O(0, 0): Z = 3(0) + 2(0) = 0$At $A(0, 16/3): Z = 3(0) + 2(16/3) = 32/3 \approx 10.67$At $B(5, 2): Z = 3(5) + 2(2) = 15 + 4 = 19$At $C(7, 0): Z = 3(7) + 2(0) = 21$Comparing these values,the maximum value of $Z$ is $21$ at point $C(7, 0)$.

The maximum value of the objective function $Z = 3x + 2y$ for the linear constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,$y \geq 0$ is

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