Hint for Practice Exercise 4:

 

This chart represents a variety of student counts and the income created by each. The chart illustrates school income increasing to 200 students and decreasing after 250 students. At the extreme values of the chart, 0 and 450 students, the school income is 0. Therefore, there is a maximum income value for the school on the closed interval [0, 450]. At closer inspection, the maximum income will within the closed interval of [200, 250].

Number of Students

Cost per Student

School Income

0

$15

$0

100

15

1500

150

15

2250

150 + 50 = 200

12.50

2500

150 + 100 = 250

10

2500

150 + 150 = 300

7.50

2250

150 + 250 = 400

2.50

1000

150 + 300 =450

0

0