Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: selling x hundred LCD TVs is given by R(x) = −5x3 + 35x2 + 155x for x ≥ 0, while the cost, in thousands of dollars, to produce x hundred LCD TVs is given by C (x) = 200x + 25 for x ≥ 0. How many TVs, to the nearest TV, should be produced to make a profit? Solution. Recall that profit = revenue − cost. If we let P denote the profit, in thousands of dollars, which results from producing and selling x hundred TVs then P (x) = R(x) − C (x) = −5x3 + 35x2 + 155x − (200x + 25) = −5x3 + 35x2 − 45x − 25, where x ≥ 0. If we want to make a profit, then we need to solve P (x) > 0; in other words, −5x3 + 35x2 − 45x − 25 > 0. We have yet to discuss how to go about finding the zeros of P , let alone making a sign diagram for such an animal,4 as such we resort to the graphing calculator. After finding a suitable window, we get We are looking for the x values for which P (x) > 0, that is, where the graph of P is above the x-axis. We make use of the ‘Zero’ command and find two x-intercepts. 4 The procedure, as we shall see in Chapter 3 is ident...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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