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 =−16 𝑡 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 =−16 𝑡 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+0.6 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?

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+0.6 𝑥 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?