Question

Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \] 

Hint:

In linear programming, the optimal solution occurs at one of the corner points of the feasible region.

Answer 1

Step 1: Graph the constraints to form the feasible region. 

Step 2: The objective function is \( Z = 5x + 3y \). Find the corner points of the feasible region. 

Step 3: Evaluate \( Z \) at each corner point. 

Step 4: Choose the corner point that gives the minimum value of \( Z \).