Question

A linear programming problem is shown below:

$\text{Maximize 3x + 7y}$

$\text{Subject to}$

$3x+7y\le 10$
$4x+6y\le 8$
$x,y\ge 0$

$\text{It has}$

• A. exactly one optimal solution
• B. infinitely many optimal solution
• C. an unbounded objective function
• D. exactly two optimal solution

Answer 1

The correct option is A exactly one optimal solution

$\text{Max.}3x+zy$

$\text{Subjected to:}$

$3x+7y\le 10$

$4x+6y\le 8$

$x,y\ge 0$



$\text{At point A, (2, 0),}$

$\text{z = 3 × 2 + 7 × 0 = 6}$

$\text{At point B}(0,\frac{4}{3})$

$z=3\times 0+7\times \frac{4}{3}=\frac{28}{3}=9.33$

$\text{Hence, it has exactly one optimal solution.}$