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.
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.
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Evaluate $x+y$ at each corner of the feasible region.
Updated On: Oct 1, 2026
- \((47.5,0)\)
- \((0,95)\)
- \((0,35)\)
- \((40,15)\)
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The Correct Option is D
Solution and Explanation
Step 1: Corner points
The constraints are \(x+2y\le70\) and \(2x+y\le95\) with \(x,y\ge0\).
Corners: \((0,0)\), \((47.5,0)\), \((0,35)\), and the intersection of \(x+2y=70\) and \(2x+y=95\).
Step 2: Intersection
Solve: \(x=40\), \(y=15\).
Step 3: Compare values
\((0,0)\): \(0\). \((47.5,0)\): \(47.5\). \((0,35)\): \(35\). \((40,15)\): \(55\).
The maximum is \(55\) at \((40,15)\). Option (D).
Final Answer:
The maximum occurs at \((40,15)\), option (D). \[ \boxed{\text{(D) }(40,15)} \]
The constraints are \(x+2y\le70\) and \(2x+y\le95\) with \(x,y\ge0\).
Corners: \((0,0)\), \((47.5,0)\), \((0,35)\), and the intersection of \(x+2y=70\) and \(2x+y=95\).
Step 2: Intersection
Solve: \(x=40\), \(y=15\).
Step 3: Compare values
\((0,0)\): \(0\). \((47.5,0)\): \(47.5\). \((0,35)\): \(35\). \((40,15)\): \(55\).
The maximum is \(55\) at \((40,15)\). Option (D).
Final Answer:
The maximum occurs at \((40,15)\), option (D). \[ \boxed{\text{(D) }(40,15)} \]
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