Answer:
(View Below)
Explanation:
I cannot directly create or display graphs, but I can describe how you can set up the equations and explain which type of graph represents this situation.
Let's use x to represent the number of hours you work at job 1 and y to represent the number of hours you work at job 2.
Here are the constraints:
1. You work no more than 12 hours a week: This can be represented as \(x + y \leq 12\).
2. The first job pays you $8 an hour, and the second job pays you $10 an hour. So, the total weekly earnings (\(E\)) can be represented as \(E = 8x + 10y\).
3. You must earn at least $100 each week: This can be represented as \(E \geq 100\).
So, to summarize, you have the following system of inequalities:
\[
\begin{align*}
x + y & \leq 12 \\
8x + 10y & \geq 100
\end{align*}
\]
To graph this situation, you would plot the lines representing the equalities:
1. The line \(x + y = 12\) represents the constraint on the total number of hours you work.
2. The line \(8x + 10y = 100\) represents the constraint on your total earnings.
The feasible region (where both inequalities are satisfied) is the area below or on the left side of the line \(x + y = 12\) and above or on the right side of the line \(8x + 10y = 100\). This region represents the combinations of hours at job 1 and job 2 that meet the requirements.
You would typically graph this on a coordinate plane to visualize it better. The feasible region would be a shaded area on the graph, and you can identify the solutions within this region that satisfy both constraints.