MHT CET · Maths · Linear Programming
The maximum value of \(z=10 z+25 y\) subject to \(0 \leq x \leq 3\), \(0 \leq y \leq 3, x+y \leq 5\) occurs at the point.
- A \((3,2)\)
- B \((2,3)\)
- C \((4,3)\)
- D \((5,4)\)
Answer & Solution
Correct Answer
(B) \((2,3)\)
Step-by-step Solution
Detailed explanation
Required area is shaded.
Vertices of the required region are \(0(0,0)\);
\(
\mathrm{A}(3,0) ; \mathrm{B}(3,2) ; \mathrm{C}(2,3) ; \mathrm{D}(0,3)
\)
We have to maximize objective function
\(
\begin{array}{lll}
\mathrm{Z}=10 \mathrm{x}+25 \mathrm{y} & \\
\therefore \quad & \mathrm{Z}_{(\mathrm{O})}=0+0 & =0 \\
\mathrm{Z}_{(\mathrm{A})} & =30+0 & =30 \\
\mathrm{z}_{(\mathrm{B})} & =30+50 & =80 \\
\mathrm{Z}_{(\mathrm{C})} & =20+75 & =95 \\
\mathrm{z}_{(\mathrm{D})} & =0+75 & =75
\end{array}
\)
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