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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