Sec 2.5 – Max/Min Problems – Business and Economics Applications
1) The sum of two numbers is 70. What are the numbers if their
product is a maximum?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
2) A cardboard box manufacturing company has to maximize the volume
of a box made from a 24-inch by 9-inch sheet of cardboard. What are
the dimensions of the box?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
3) The position function of a projectile launched vertically upward from
an elevated position is 𝑠 𝑡 = −16𝑡 2 + 87𝑡 + 129. Position (s) is
measured in feet and time (t) is measured in seconds.
a) When will the projectile hit the ground?
b) What is the impact velocity?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
3) The position function of a projectile launched vertically upward from
an elevated position is 𝑠 𝑡 = −16𝑡 2 + 87𝑡 + 129. Position (s) is
measured in feet and time (t) is measured in seconds.
c) When will the projectile reach its maximum height?
d) What is its maximum height?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
4) A box is to be constructed where the base length is 3 times the base
width. The material used to build the top and bottom cost $10 per
square foot and the material used to build the sides cost $6 per square
foot. If the box must have a volume of 50 cubic feet, determine the
dimensions that will minimize the cost to build the box.
Sec 2.5 – Max/Min Problems – Business and Economics Applications
5) A printer needs to make a poster that will have a total area of 200 in2
and will have 1 inch margins on the sides, a 2 inch margin on the top
and a 1.5 inch margin on the bottom. What dimensions will give the
largest printed area?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
6) The price function for an appliance is 𝑝 = 280 − 0.4𝑥, where x
represents the number of appliances sold. The cost function for
producing x number of appliances is 𝐶 𝑥 = 5000 + 0.6𝑥 2 .
What is the revenue function, R(x)?
What is the profit function, P(x)?
How many appliances must be sold in order to maximize the profit?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
6) The price function for an appliance is 𝑝 = 280 − 0.4𝑥, where x
represents the number of appliances sold. The cost function for
producing x number of appliances is 𝐶 𝑥 = 5000 + 0.6𝑥 2 .
What is the maximum profit?
What price per appliance must be charged in order to maximize the
profit?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
7) When 30 orange trees are planted on an acre, each will produce 500
oranges a year. For every additional orange tree planted, each tree will
produce 10 fewer oranges. How many trees should be planted to
maximize the yield?
Sec 2.5 – Max/Min Problems – Business and Economics Applications
8) A farmer wishes to enclose 3000 square feet with 6 compartments of
equal area. What dimensions would minimize the amount of the
fencing?