Question

The point at which the maximum value of \(x+y\) subject to constraints \(x+2y\leq 70\) and \(2x+y\leq 95,x\geq 0,y\geq 0\) is.

• A. \((47.5,0)\)
• B. \((0,95)\)
• C. \((0,35)\)
• D. \((40,15)\)

Hint:

Evaluate $x+y$ at each corner of the feasible region.

Answer 1

The Correct Option is D

Step 1: Use the objective line
Slide the line $x+y=k$ outward. The last point touched in the feasible region is the corner where the two constraints cross, $(40,15)$.
It gives $k=55$, more than $47.5$ and $35$. Option (D).

Final Answer:
Option (D). \[ \boxed{\text{(D)}} \]