120118 Quiz 5.1-5.5 Review - Answers

Let n represent the number of shirts orderedsold

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A student group decides to produce and sell T-Shirts as a fundraiser. Let n represent the number of shirts ordered/sold during the fundraiser.
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Name Honors Algebra 2 January 17, 2012 Quiz Review 5.1-5.5 page 4 a. The group’s costs are a fixed cost of $50 for the template plus $9 a shirt. Write a function C ( n ) for the cost of ordering n t-shirts. C ( n ) = 50 + 9 n b. The group decides that if it receives orders for n t-shirts, the selling price for each shirt will be (25 – n ) dollars. Write a function R ( n ) for the revenue from selling n shirts. R ( n ) = n (25 – n ) c. Profit is found by subtracting costs from revenue. Write a profit function P ( n ), then simplify it as much as possible. P ( n ) = R(n) – C(n) d. For what values of n would this fundraiser be profitable? Show or tell how you get your answer. This means find the zeros of P(n) . Solve for n using any method, I used quadratic formula. So the fundraiser will be profitable if they sell between 5 and 11 shirts . e. For what number of shirts would this fundraiser be the most profitable? Show or tell how you get your answer. Maximum is at the vertex, so use So they will make the most profit if they sell 8 t-shirts . This is also half way between 5 and 11 (the two zeros).
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