Question

Jessie works at least 36 hours a week. She works as a math

tutor and as a teacher. The number of hours Jessie works as a teacher (y) is at
least twice the number of hours she works as a tutor (x).
Write the set of inequalities that represents the constraints of the
situation and state a point (x, y) that is part of the feasible region.​

Answer 1

The feasible region is unbounded which is the shaded portion in the graph.

Explanation:

Given that, the number of hours Jessie works as a teacher and tutor is y and x respectively, which can't be negative.

So,
`x\ge0\;\cdots(i)`

y\ge0\;\cdots(ii)

She works at least 36 hours a week.

`\Rightarrow x+y\ge 36`

`\Rightarrow y\ge 36-x\;\cdots (iii)`

She works as a teacher for al least twice the number of hours she works as a tutor.

`\Rightarrow y\ge2x\;\cdots(iv)`

The boundary of the inequalities from equations (i), (ii), (iii), and (iv) are

`x=0, y=0, y=36-x` and
`y=2x`.

The feasible region is the shaded portion which is the unbounded region as shown in the graph. Any point P(x,y) from the feasible region will satisfies all the constraints.