Question

The optimal value of the objective function is attained at the point is

• A. Given by the intersection of inequations with axes only
• B. Given by the intersection of inequations with X-axis only
• C. Given by corner points of the feasible region
• D. None of the above

Answer 1

The correct option is C

Given by corner points of the feasible region

Explanation for the correct option

The optimal value is obtained from the intersection of the inequalities or the given constraints under the feasible region

For example,

Let $\mathrm{Max}\left(\mathrm{Z}\right)=3\mathrm{x}+4\mathrm{y}$

subjected to constrains

$$\begin{gathered} x+y\le 1 \\ x\ge 0 \\ y\ge 0 \end{gathered}$$

The feasible region is the shaded region.

Extreme points of the feasible region	$\mathrm{Max}\left(\mathrm{Z}\right)=3\mathrm{x}+4\mathrm{y}$
$A\left(1,0\right)$	$3$
$B\left(0,1\right)$	$4$
$O\left(0,0\right)$	$0$

Therefore $\mathrm{Max}\left(\mathrm{Z}\right)=4$

Hence, the correct option is $\left(\mathrm{C}\right)$: Given by corner points of the feasible region.