Question
What will be the minimum cost?
✓
Answer
We have minimize z = 400x + 200y, subject to
$5\text{x}+2\text{y}\geq30$
$2\text{x}+\text{y}\leq15$
$\text{x}\leq\text{y}$
$\text{x}\geq0,\text{y}\geq0$
These inequalities are plotted as shown in the adjucent figure.
From the figure shaded region is bounded with the corner points $\text{A}\Big(\frac{30}{7},\frac{30}{7}\Big),$ B(5, 5) and C(0, 15).
| Corner points | Corresponding value of Z = 400x + 200 |
| $(0, 15)$ | $3000$ |
| $(5,5)$ | $3000$ |
| $\Big(\frac{30}{7},\frac{30}{7}\Big)$ | $400\times\frac{30}{7}+200\times\frac{30}{7}=\frac{18000}{7}=2571.43$ (Minimum) |
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