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Previous Year Question (PYQs)



$Z = 7x + y$, subject to constraints: $5x + y \ge 5,\ x + y \ge 3,\ x \ge 0,\ y \ge 0.$ Then minimum value of $Z$ occurs at –





Solution

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 $(0,5)$


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