Question:
Maximise Z = 5x + 3y
subject to $3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0$.
Solution:
The feasible region determined by the system of constraints, $3 x+5 y \leq 15$,
$5 x+2 y \leq 10, x \geq 0$, and $y \geq 0$, are as follows.
The corner points of the feasible region are $\mathrm{O}(0,0), \mathrm{A}(2,0), \mathrm{B}(0,3)$, and $\mathrm{C}\left(\frac{20}{19}, \frac{45}{19}\right)$.
The values of Z at these corner points are as follows.
Therefore, the maximum value of $Z$ is $\frac{235}{19}$ at the point $\left(\frac{20}{19}, \frac{45}{19}\right)$.
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