Question

A system has the following constraints: x + y ≥ 80 3x + 2y ≤ 360 x + 2y ≤ 200 x ≥ 0 y ≥ 0 Which graph represents the feasible region for the system?

Answer 1

We are given system with the following constraints:

x + y ≥ 80 ( it will be a line passing through (80,0) and (0,80) with shaded region above the line)

3x + 2y ≤ 360 ( it will be a line passing through (120,0) and (0,180) and shaded region will be below the line i.e. towards the origin)

x + 2y ≤ 200 ( it will be a line passing through (200,0) and (0,100) and shaded region will lie below the line i.e. towards the origin)

x ≥ 0

y ≥ 0

Clearly from the information we could see that the feasible region will lie in the first quadrant.

Since both x and y are greater than equal to zero.

The feasible region will be a pentagon abcde as could bee seen in the graph.

Answer 2

we have that

x + y ≥ 80
3x + 2y ≤ 360
x + 2y ≤ 200
x ≥ 0
y ≥ 0

using a graph tool
see the attached figure


the solution is the shaded graph----------> see the attached figure