Question

The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] is:

• A. 5
• B. 4
• C. 6
• D. 3

Hint:

Always graph the inequality constraints and evaluate at the feasible points to find the maximum or minimum value.

Answer 1

The Correct Option is D

We are given the following constraints: \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] First, plot the constraint line \( 2x + 3y = 6 \) and find the feasible region. We also need to maximize \( x + y \). The intersection of \( 2x + 3y = 6 \) with the axes is at:
- \( x = 3, y = 0 \) for the x-intercept.
- \( x = 0, y = 2 \) for the y-intercept. By evaluating at different points in the feasible region, we can see that the maximum value of \( x + y \) occurs at \( x = 1, y = 2 \), giving a value of \( x + y = 3 \). Thus, the maximum value is 3.