Finding The Maximum Using The Vertex Worksheet With Answer Key Page 4
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5Word Problem questions for students to try:
#1. Cathy has 48m of fencing to make a rectangular pen for her pet. What is the maximum
2
area? Answer: 144m
Let x = width
Let 24-x = length
(P = 2L + 2W
48 = 2L + 2W
24 = L + W L = 24 – W)
A = x(24-x)
2
A = 24x – x
2
A = -x
+ 24x
Find vertex (p, q) to find maximum Area.
b
24
= − = −
=
p
12
−
2a
2( 1)
2
q = -(12)
+ 24(12)
q = -144 + 288
2
q = 144
So the maximum area = 144m
#2. The Summer Theatre charges $10 per ticket and it has had a full house of 500 nightly. The
manager estimates that the ticket sales would decrease by 50 for each $2 increase in ticket
cost. What is the most profitable price to charge for each ticket? At this new price what is the
maximum revenue the Summer Theater can expect to generate?
Answer: ticket price = $15
max revenue = $5625
Let x = number of $2 increases
Let R = revenue
R = price x numberoftickets
R = (10 + 2x)(500 – 50x)
2
R = 5000 – 500x + 1000x – 100x
2
R = -100x
+ 500x + 5000
Find vertex (p, q) to find the Max revenue.
b
500
= − =
−
=
p
2.5
−
2a
2( 100)
2
q = -100(2.5)
+ 500(2.5) + 5000
q = 5625
The Max revenue is $5625 .
The price is 10 + 2(2.5) = $15 per ticket
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