The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of…
- $19.5$
- $2$
- $195$
- $19.8$
Solution
Let the corner points of the feasible region be A, $\mathrm{B}, \mathrm{C}, \mathrm{D}$.
Solving equations $y=, 3$ and $2 x+3 y=12$, we get
$\mathrm{A}=(1.5,3)$
Similarly,
$\begin{aligned}
& \mathrm{B}=(4,3) \\
& \mathrm{C}=(4,7) \\
& \mathrm{D}=\left(\frac{3}{5}, \frac{18}{5}\right)
\end{aligned}$
Let $Z=3 x+5 y$
$\therefore \quad$ Value of $Z$ at point $A=19.5$
Value of $Z$ at point $B=27$
Value of $Z$ at point $C=47$
Value of $Z$ at point $D=\frac{99}{5}$
$\therefore \quad$ The minimum value of $Z$ is 19.5 .Asked in: MHT CET 2023 (10 May Shift 2)