The difference between the maximum and minimum values of the objective function $Z = 3x+5y$, subject to the constraints $x+3y\leq 60$, $x+y\geq 10$, $x-y\leq 0$, $x,y\geq 0$ is

Question

The integral $ I = \int_{\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x + \frac{\pi}{4}}{2 - \cos 2x} \, dx $ is equal to:

Answer 1

Step 1: Region
The region is bounded by $x \geq 0$, $y \geq x$, $x + y \geq 10$ and $x + 3y \leq 60$.

Step 2: Vertices
$(0,10)$, $(5,5)$, $(15,15)$, $(0,20)$.

Step 3: Values
$Z = 50, 40, 120, 100$ respectively. Max $-$ min $= 120 - 40 = 80$. Option (D).

Final Answer:
Option (D). \[ \boxed{80} \]

The difference between the maximum and minimum values of the objective function \(Z = 3x+5y\), subject to the constraints \(x+3y\leq 60\), \(x+y\geq 10\), \(x-y\leq 0\), \(x,y\geq 0\) is

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The Correct Option is D

Solution and Explanation

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