Exercise 17 Page 149

We will first write a system of inequalities. Let x be the number of hours working at the Pizza Palace and y be the number of hours working at a car wash. We have been told that he cannot work more than 25 hours per week. Thus, he cannot work more than 25* 8= 200 hours in 8-week period.

Now we have two inequalities to write a system x+y≤ 200 & (I) 9x+12y ≥ 925 & (II) Let's begin by graphing Inequality I. We will first find the boundary line by replacing the inequality sign with the equals sign. cc Inequality I &Boundary Line I x+y ≤ 200 & x+y = 200We will graph the boundary line by finding its intercepts. We will substitute y for 0 for the x-intercept and x for 0 for the y-intercept.

Now that we know the intercepts of the boundary line, we can plot the intercepts and draw a line that passes through the them. Notice that the number of working hours cannot be negative, so the line will be bound by the axes. It will also be solid because the inequality is non-strict.

Next, we will test an arbitrary point to decide which region we should shade. Let's test the point (0,0).

The point satisfied the inequality, so we will shade the region that contains the point.

To graph the second inequality, we will think the same way. cc Inequality II &Boundary Line II 9x+12y ≥ 925 & 9x+12y = 925 Let's begin by finding the intercepts of the boundary line. We will substitute y for 0 for the x-intercept and x for 0 for the y-intercept.

Now the boundary line can be graphed.

We will again test the point (0,0) to complete the graph.

The point did not satisfy the inequality, so we will shade the region that does not contain the point.

The overlapping section of the graph above is the solution set to the system.