Question

Which graph best represents the feasibility region for the system in the picture?See image for system.See image for possible graphs.

Answer 1

Given the system of inequalities:

`\begin{gathered} x\ge0 \\ y\leq-(1)/(8)x+5 \\ y\ge(5)/(8)x-1 \end{gathered}`

Graph the inequalities.

First, shade the region of first inequality.

To shade the second inequality, draw the line

`y=-(1)/(8)x+5`

When x = 0, y = 5 and when y = 0, x = 40.

Mark the points (0,5) and (40,0) and join the points to draw the line.

Shade the inequality.

Now, draw the next inequality.

To draw the third inequality, first draw the line

`y=(5)/(8)x-1`

When x = 0, y = -1 and when y = 0, x = 8/5. Mark the points and join it to get the required line.

Shade the region correspondity to its inequality.

This is the feasible region. From the options, option C is correct.