Question

The linear programming problem minimise $Z=3 x+2 y$
subject to the constraints
$x+y \geq 8$
$3 x+5 y \leq 15$
$x \geq 0, y \geq 0 \text { has }$

• A. one solution
• B. no feasible solution
• C. two solutions
• D. infinitely many solutions

Answer 1

Answer: (B)

Given that,
Minimise $Z=3 x+2 y$
Subject to the constraints are
$x+y \geq 8$ ...(i)
$3 x+5 y \leq 15 $...(ii)
$x \geq 0, y \geq 0$...(iii)
Let us graph the inequalities (i) to (iii).

From figure, you can see that there is no point satisfying all the constraints simultaneously. Thus, the problem is having no feasible region and hence no feasible solution.