Question

The minimum value of \(z = 3x+5y\), subject to constraints \(x\leq 80\), \(y\geq 60\), \(x+y\leq 200\) & \(x,y\geq 0\) occurs at the point...

• A. \((0,200)\)
• B. \((60,0)\)
• C. \((0,60)\)
• D. \((80,60)\)

Hint:

Find the corner points of the feasible region and compare z at each.

Answer 1

The Correct Option is C

Step 1: Think about the objective
Both coefficients are positive, so z is smallest where both x and y are as small as the constraints allow.

Step 2: Lowest corner
The lowest allowed $y$ is $60$ and the lowest $x$ is $0$, giving $(0,60)$ and $z = 300$. Every other corner gives a larger value. Option (C).

Final Answer:
(0, 60). \[ \boxed{\text{(C)}\ (0,60)} \]