The difference between the maximum value and the minimum value of the objective function $z = 3x+y$ subject to the constraints $2x+3y\leq 6$, $x+y\geq 1$, $x\geq 0$, $y\geq 0$ 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: Sketch:
The region lies below the line $2x + 3y = 6$, above the line $x + y = 1$, in the first quadrant. It is a quadrilateral.

Step 2: Pick the extreme corners:
Since $z = 3x + y$ grows fastest in $x$, the maximum is at the corner with the largest $x$, namely $(3,0)$, $z = 9$. The minimum is at the corner closest to the origin in the $y$ direction, $(0,1)$, $z = 1$.

Step 3: Difference:
$9 - 1 = 8$.

Final Answer:
The difference is 8, option (C). \[ \boxed{8} \]

The difference between the maximum value and the minimum value of the objective function \(z = 3x+y\) subject to the constraints \(2x+3y\leq 6\), \(x+y\geq 1\), \(x\geq 0\), \(y\geq 0\) is....

Show Hint

The Correct Option is C

Solution and Explanation

Top Questions on Linear Programming

Questions Asked in MHT CET exam