MHT CET · Maths · Mathematical Induction
The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function \(3 x+5 y\), subject to the linear constraints given by this system of inequations is
- A \(19.5\)
- B \(2\)
- C \(195\)
- D \(19.8\)
Answer & Solution
Correct Answer
(A) \(19.5\)
Step-by-step Solution
Detailed explanation
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 \(D=\frac{99}{5}\)
\(\therefore\) The minimum value of \(Z\) is 19.5 .
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