MHT CET · Maths · Linear Programming
The maximum value of the objective function \(Z=3 x+2 y\) for linear constraints \(x+y \leq 7\) \(2 x+3 y \leq 16, x \geq 0, y \geq 0\) is
- A 16
- B 21
- C 25
- D 28
Answer & Solution
Correct Answer
(B) 21
Step-by-step Solution
Detailed explanation
The feasible region is \(O A B C O\).
At \(O(0,0), Z=0\)
At \(A\left(0, \frac{16}{3}\right), Z=\frac{32}{3}\)
At \(B(5,2), Z=15+4=19\)
At \(C(7,0), Z=21\)
\(\therefore\) Maximum value of \(Z\) is 21 .
At \(O(0,0), Z=0\)
At \(A\left(0, \frac{16}{3}\right), Z=\frac{32}{3}\)
At \(B(5,2), Z=15+4=19\)
At \(C(7,0), Z=21\)
\(\therefore\) Maximum value of \(Z\) is 21 .
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