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 k(x) = -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). c) 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 g(x) = 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.

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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.