The minimum value of the objective function $z=4 x+6 y$ subject to $x+2 y \geq 80,3 x+y \geq 75, x, y \geq 0$ is

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Aicharya · Accepted Answer

Refer figure Required area is shaded. Vertices of feasible region are $\mathrm{A}=(80,0) ; \mathrm{C}=(0,75)$ and point of intersection of given lines is $\mathrm{B}=(14,33)$ We have to minimize objective function $\mathrm{z}=4 \mathrm{x}+6 \mathrm{y}$ $\begin{aligned} & 	herefore \quad \mathrm{Z}_{(\mathrm{A})}=4(80)+6(0)=320 \ & \mathrm{Z}_{(\mathrm{B})}=4(14)+6(33)=254 \ & \mathrm{Z}_{(\mathrm{C})}=4(0)+6(75)=450 \ & \end{aligned}$

The minimum value of the objective function $z=4 x+6 y$ subject to $x+2 y \geq 80,3 x+y \geq 75, x, y \geq…

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