Judy has agreed to teach a ceramics class at a community art center if the enrol
ID: 3404931 • Letter: J
Question
Judy has agreed to teach a ceramics class at a community art center if the enrollment is at least 14 students, but not more than 35 students. If the enrollment is 14, she will charge every student a price of $90. Otherwise, for each student in excess of 14, she will lower the price of every student $3. So, for example, if she gets 2 extra students, then the price for every student will drop $6. Let x be the number of students enrolled in the class. Find a function p(x) that expressed the price that each student pays as a function of the number of students in the class. Find a function R(x) that expresses the revenue that Judy will receive as a function of the number of students in the class. What enrollment maximizes the revenue? How much will each student pay? How much revenue will Judy make?Explanation / Answer
a)
Since the number of students must be atleast 14 and not more than 35
Let the number of students
P(x) = 90$, if x = 14
P(x) = 90 -3(x-14), 14 <= x <= 35
(x-14) represents the number of students more than 14, since Judy is dropping rate by $3 per student, hence we need to multiply it with -3
P(x) = 90 - 3x + 42
P(x) = 132 - 3x
b)
R(x) = Number of students * P(x)
=> x * (132 - 3x)
=> 132x - 3x^2
c)
Differentiatiing the function R(x) wrt x we get
R'(x) = 132 - 6x
Equating the derivative to zero, we get
132 = 6x
x = 22
Hence enrollment of 22 students maximizes the revenue
Each student will pay
P(22) = 132 - 3(22) = 132 - 66 = 66$
Revenue Judy will make
=> x * P(x)
=> 22 * 66
=> 1452$
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