The feasible region for an LPP is shown in the given figure. The maxi…

The correct answer is Option (2) → 100

The feasible region is the shaded quadrilateral OABC. Its corners are O(0, 0), A(25, 0), C(0, 20) and B, where the two lines meet.

The line through D(0, 50) and A(25, 0) is \(2x+y = 50\); the line through C(0, 20) and (40, 0) is \(x+2y = 40\). Solving them together:

    \(2x+y = 50\), \(x+2y = 40\)
    \(3x+3y = 90\), so \(x+y = 30\)
    \(x = 20,\ y = 10\)

So B = (20, 10). By the corner point method, values of z = 3x + 4y:

    \(z(0, 0) = 0\)
    \(z(25, 0) = 75\)
    \(z(20, 10) = 60+40 = 100\)
    \(z(0, 20) = 80\)

The maximum value is 100, at B(20, 10).