Question

Consider a linear programming problem with two variables and two constraints. The objective function is to maximize $x_1+x_2.$ The corner points of the feasible region are (0, 0), (0, 2), (2, 0) and (4/3, 4/3)

If an additional constraint $X_1+X_2\le 5$ is added, the optimal solution is

• A. $(5,0)$
• B. $(5/2,5/2)$
• C. $(5/3,5/3)$
• D. $(4/3,4/3)$

Answer 1

The correct option is D $(4/3,4/3)$



$\text{At point A (2, 0), z = 1 × 2 + 1 × 0 = 2}$

$\text{At point B,}(\frac{4}{3},\frac{4}{3}),z=1\times \frac{4}{3}+1\times \frac{4}{3}$

$\text{At point C, (0, 2) = 1 × 0 + 1 × 2 = 2}$

$\text{Constant equation}{x}_1+x_2\le 5\text{has no effect on optimal region.}$

$\text{So, maximum value of z occurs at point}B(\frac{4}{3},\frac{4}{3})$