Question
What will be the minimum cost?
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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).
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Corner points
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Corresponding value of Z = 400x + 200
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$(0, 15)$
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$3000$
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$(5,5)$
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$3000$
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$\Big(\frac{30}{7},\frac{30}{7}\Big)$
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$400\times\frac{30}{7}+200\times\frac{30}{7}=\frac{18000}{7}=2571.43$ (Minimum)
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