$Z = 7x + y$, subject to constraints:
$5x + y \ge 5,\ x + y \ge 3,\ x \ge 0,\ y \ge 0.$
Then minimum value of $Z$ occurs at –
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Solution:
Corner points by solving the constraints:
$(0,5),\ (3,0),\ \left(\frac{1}{2},\frac{5}{2}\right)$
Now compute $Z = 7x + y$:
At $(0,5): Z = 5$
At $(3,0): Z = 21$
At $\left(\frac{1}{2},\frac{5}{2}\right): Z = \frac{7}{2} + \frac{5}{2} = 6$
Minimum $Z = 5$ at $(0,5)$