Question

Problem 1: An ice cream shop finds that its weekly profit P (measured in dollars) as a function of the price x (measured in dollars) it charges per ice cream cone is given by the function k, defined by kx)-125x2 +670x 125 where P k(x). a) Determine the maximum weekly profit and the price of an ice cream cone that produces that maximum profit b) The cost of the ice cream cone is too low then the ice cream shop will not make a profit. Determine what the ice cream shop needs to charge in order to break even (make a profit of $0.00) ) If the cost of the ice cream cone is too high then not enough people will want to buy ice cream. As a result, the weekly profit will be $0.00. Determine what the ice cream shop would have to charge for this to happen (the profit to be $0.00) d) The profit function for Cold & Creamy (another ice cream shop) is defined by the function g where gx)- k(x-2). Does the function g have at the same maximum value as k? What is the price per ice cream cone that Cold & Creamy ice cream shop must charge to produce a maximum profit? Explain. Describe the meaning of h(x) = k(x)-125 and then compare/contrast the maximum value for each function e)

Answer 1

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