Question

The maximum value of Z = 10x + 16y, subject to constraints $ x \geq 0, \quad y \geq 0, \quad x + y \leq 12, \quad 2x + y \leq 20 $

• A. 144
• B. 192
• C. 120
• D. 240

Hint:

In linear programming, always plot the feasible region and find the vertices of the region to maximize or minimize the objective function.

Answer 1

The Correct Option is B

Given, the constraints: \[ x \geq 0, \quad y \geq 0, \quad x + y \leq 12, \quad 2x + y \leq 20 \] 
The feasible region is \(OABC\). We now find the values of \(x\) and \(y\) that maximize \(Z = 10x + 16y\) under these constraints. By solving the system of inequalities, the optimal solution occurs at the point where \(x = 8\) and \(y = 4\). 
Substituting these values into the objective function: \[ Z = 10(8) + 16(4) = 80 + 64 = 192 \]