Question

Consider the following LPP: Maximise \( Z = 9x + 3y \) Subject to the constraints: \[ x + 3y \leq 60, \quad x - y \leq 0, \quad x \geq 0, \quad y \geq 0 \] If \( x = A, y = B \) is the optimum solution of the given LPP, then the value of \( A + B \) is:

• A. 15
• B. 30
• C. 48
• D. 61

Answer 1

The Correct Option is B

Graph the constraints to identify the feasible region. The vertices of this region are the intersection points of the lines: \(x + 3y = 60, \quad x - y = 0, \quad x = 0, \quad y = 0.\)

The vertices are \((0, 0), (0, 20), (15, 15)\). Calculate \(Z = 9x + 3y\) at these vertices:

\[ Z(0, 0) = 0, \quad Z(0, 20) = 60, \quad Z(15, 15) = 135. \]

The maximum value of \(Z\) is 135, occurring at \((15, 15)\). Therefore, \(A = 15\) and \(B = 15\). The sum \(A + B\) is:

\[ A + B = 15 + 15 = 30. \]