1) The sum of two numbers is 70. What are the numbers if their product is a maximum? Sec 2.5 –...
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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
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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
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Sec 2.5 – Max/Min Problems – Business and Economics Applications3) The position function of a projectile launched vertically upward from an elevated position is . 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?
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Sec 2.5 – Max/Min Problems – Business and Economics Applications3) The position function of a projectile launched vertically upward from an elevated position is . Position (s) is measured in feet and time (t) is measured in seconds.
d) What is its maximum height?
c) When will the projectile reach its maximum height?
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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
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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
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Sec 2.5 – Max/Min Problems – Business and Economics Applications6) The price function for an appliance is where x represents the number of appliances sold. The cost function for producing x number of appliances is .
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?
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Sec 2.5 – Max/Min Problems – Business and Economics Applications6) The price function for an appliance is where x represents the number of appliances sold. The cost function for producing x number of appliances is .
What is the maximum profit?
What price per appliance must be charged in order to maximize the profit?
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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
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Sec 2.5 – Max/Min Problems – Business and Economics Applications8) A farmer wishes to enclose 3000 square feet with 6 compartments of equal area. What dimensions would minimize the amount of the fencing?