Solve the following linear programming problem graphically : Maxi… - Vidyadip

Question

Solve the following linear programming problem graphically :
Maximise Z = 34x + 45y
under the following constraints
x + y $\leq$ 300
2x + 3y$\leq$ 70
x $\geq$ 0, y $\geq$ 0

✓

Answer

Maximise: z = 34x + 45y subject to x + y $\leq$ 300,
2x + 3y $\leq$ 70, x $\geq$ 0, y $\geq$ 0
Plotting the two lines.
Correct shading
$\text{Z(A)}=\text{Z}\Big(0,\frac{70}{3}\Big)=1050$
$\text{Z(B)}=\text{Z}(35,0)=1190$
⇒ max (1190) at x = 35, y = 0.

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