(Solved): 1. Miss Kito is a huge fan of the Jurassic Park movies. When the first movie was released, she decid ...

1. Miss Kito is a huge fan of the Jurassic Park movies. When the first movie was released, she decided to try to capitalize off the success of the movie by selling novelty mosquitos trapped in amber. She called her entrepreneurial endeavor Miss Kito's Mosquitos. A market study showed that the demand for her item was based on the equation: \( q=224-14 p \) where \( q \) represents the number of mosquitos sold each week based on a price, \( p \), in dollars. The cost to produce each mosquito is \( \$ 3 \). \( ( \) So, \( C=3 q) \) Miss Kito wants to determine at what price point she should sell the mosquitos in order to maximize her weekly Profit. (Note: Revenue is the money made strictly from sales of the item. So, \[ \text { Revenue }=\text { price } \text { * quantity sold } \rightarrow R=p q \text { ) } \] a) [4 pts] Create the Profit function strictly in terms of price, \( p \). \[ \text { Hint: } \text { Profit = revenue }-\text { cost, i.e., } P=R-C \] b) [5 pts] Determine the price at which Profit is maximized and the number of mosquitos that will be sold at this price point. Also find the Maximum Profit. If using an algebraic method for finding this Maximum point, show all work as to how you found your answer. If using your calculator, provide a detailed, labeled graph of the function and indicate on your paper what calculator capabilities you used to solve the problem. Provide your final answer for the price, the number of mosquitos and the Profit using a complete sentence with appropriate units.