The feasible region for a LPP is shown in Figure. Find the minimum value of $Z=11x+7y$.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21
Given $Z=11x+7y$
As per the given figure, ABCA is the feasible region. Corner points C(0, 3), B(0, 5) and for A,
we have to solve equations
$x+3y=9$
and $x+y=5$
Which gives $x = 3,y=2$
i.e., $A(3, 2)$
Evaluating the value of Z, we get
|
Corner points |
Value of Z |
|
A(3, 2) |
$Z=11(3)+7(2)=47$ |
|
B(0, 5) |
$Z=11(0)+7(5)=35$ |
|
C(0, 3) |
$Z=11(0)+7(3)=21$ ← Minimum |
Hence, the minimum value of Z is 21 at (0, 3).