The corner points of the feasible region of a linear programming problem are $(0, 4), (8, 0)$ and $\left(\frac{20}{3}, \frac{4}{3}\right)$. If $Z = 30x + 24y$ is the objective function, then (maximum value of $Z$ - minimum value of $Z$) is equal to:

144

The correct answer is Option (4) → 144 ##

$Z = 30x + 24y$

At $(0, 4)$, $Z = 30(0) + 24(4) = 96$ (Min)

At $(8, 0)$, $Z = 30(8) + 24(0) = 240$ (Max)

At $\left(\frac{20}{3}, \frac{4}{3}\right)$, $Z = 30 \times \frac{20}{3} + 24 \times \frac{4}{3} = 200 + 32 = 232$

$Z_{max} - Z_{min} = 240 - 96 = 144$