Answer to Question #274110 in Operations Research for luca

Question

my mother works as a tutor and a babysitter. she earns 200.00 per hour as a tutor and 100.00 per hour as a babysitter. she renders 12 hours a week. she works to get at least 2,000.00. write the system of inequalities that will represent this situation. find out at least the possible number of hours my mother works as a tutor and a babysitter in a week, by graphing

Answer 1

Suppose that mother works $x$ hours as a tutor and $y$ hours as a babysitter in a week. Then

$$x+y=12$$

$$200x+100y\geq2000$$

$$x\geq 0, y\geq 0$$

Then

$$\begin{matrix} x+y=12 \\ 2x+y\geq20\\ x\geq 0, y\geq 0 \end{matrix}$$

Mother must work at least $8$ hours to get at least 2,000.00.