MHT CET · Maths · Linear Programming
The maximum value of \(\mathrm{z}=3 x+5 y\) subject to the constraints \(3 x+2 y \leq 18, x \leq 4, y \leq 6\), \(x, y \geq 0\), is
- A \(27\)
- B \(36\)
- C \(42\)
- D \(30\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
Objective function \(\mathrm{z}=3 x+5 y\)
The comer points of the feasible region are \(\mathrm{O}(0,0), \mathrm{A}(4,0), \mathrm{B}(4,3), \mathrm{C}(2,6)\) and \(\mathrm{D}(0,6)\)
\(\therefore \quad \mathrm{Z}\) at \(\mathrm{A}(4,0)=12\)
\(\mathrm{Z}\) at \(\mathrm{B}(4,3)=27\)
\(\mathrm{Z}\) at \(\mathrm{C}(2,6)=36\)
\(\mathrm{Z}\) at \(\mathrm{D}(0,6)=30\)
\(\therefore \quad\) Maximum value of \(\mathrm{Z}\) is 36 .
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