Supplemental 5.2 Word Problems Practice
1) The sum of two numbers is 20. Find the maximum value of the product of these two
numbers.
2) The difference of two numbers is 8. The smaller of the numbers is x. Find the minimum
possible product and find the two numbers that give this product.
3) The sum of two numbers is 40. Find the greatest possible product.
4) Find two numbers such that the sum is 20 and the sum of their squares is as small as
possible.
5) A rectangle has a perimeter of 100 cm. What dimensions maximize the area of the
rectangle?
6) A rectangular enclosure has 3 sides and has a perimeter of 100 meters. What dimensions
maximize the area of the enclosure.
7) Lower Moreland wants to start a ski club. The students have found that when there are 20
members in the ski club, the dues are $8 each. For each new member recruited the dues
reduce by $0.10 for all members.
a) How much membership money would the club have if it recruited 10 new members?
What about 40 members?
b) What is the general equation that will allow you to find the total membership money
for n new members
c) How many new members should join in order to maximize membership money?
8) A plane charter company charges $60 each for 20 or fewer passengers. Each new
passenger decreases the fare by $2 per person for everyone. What is the company’s
greatest revenue?
9) Ferry charges $10 and carries 300 passengers daily. They estimate that for each $1 increase
in fares they will lose 15 passengers. What is the fare that maximizes income?
10) A ball is thrown vertically up in the air. Its height (in feet) after t seconds can be measured
by: h = 80t – 16t2
A)
B)
C)
D)
What is the height of the ball at the third second?
When does the ball obtain its maximum height?
When does the ball hit the ground?
What is the domain and range for the path of the ball?
11) A rectangular parking lot is formed by creating an entrance 12 meters wide along one side.
Find the dimensions that maximize the area if 300 m of fencing is to be used.
12) The revenue (in thousands of dollars) generated by selling x number of items can be modeled
by the function ( )
while its costs are modeled by the function
( )
A) What is the maximum revenue the business can hope to generate?
B) Use the profit function p(x) = r(x) – c(x) to determine how many items need to be sold in
order to maximize profits?
C) How many units need to be sold in order for the business to break even? (this is when
revenue = cost or profit = 0)