Solve the following linear programming problem by graphical metho… - Vidyadip

Question

Solve the following linear programming problem by graphical method. Under the following constraints :
$
\begin{aligned}
x+2 y & \geq 10 \\
x+y & \geq 6 \\
3 x+y & \geq 8 \\
x, y & \geq 0
\end{aligned}
$
$\operatorname{minimise} Z=3 x+5 y$.

✓

Answer

On drawing all the inequalities on the graph paper, ABCD is the feasible region of this problem where coordinates are as follows :
$A (0,8), B (1,5), C (2,4)$ and $D (10,0)$
Now we shall find the values of $Z$ at these points according to the following table :

Corner Point	Corresponding Value of Z = 3x + 5y
A(0, 8)	40
B (1, 5)	28
C (2, 4)	26 Minimum
D(10, 0)	30

Hence the minimum value of Z at the corner point C (2, 4) = 26.

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