1. 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?

2. 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?

3. 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 =−16 𝑡 2 +87𝑡 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?

4. 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 =−16 𝑡 2 +87𝑡 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?

5. 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.

6. 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?

7. 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 = 𝑥 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?

8. 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 = 𝑥 2 .
What is the maximum profit?
What price per appliance must be charged in order to maximize the profit?

9. 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?

10. 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?