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Example 2.3.3. The proﬁt function for a product is deﬁned by the equation Proﬁt = Revenue −
Cost, or P (x) = R(x) − C (x). Recall from Example 2.1.7 that the weekly revenue, in dollars, made
by selling x PortaBoy Game Systems is given by R(x) = −1.5x2 + 250x. The cost, in dollars, to
produce x PortaBoy Game Systems is given in Example 2.1.5 as C (x) = 80x + 150, x ≥ 0.
1. Determine the weekly proﬁt function, P (x).
2. Graph y = P (x). Include the x- and y -intercepts as well as the vertex and axis of symmetry.
3. Interpret the zeros of P .
4. Interpret the vertex of the graph of y = P (x).
5. Recall the weekly price-demand equation for PortaBoys is: p(x) = −1.5x + 250, where p(x)
is the price per PortaBoy, in dollars, and x is the weekly sales. What should the price per
system be in order to maximize proﬁt?
1. To ﬁnd the proﬁt function P (x), we subtract
P (x) = R(x) − C (x) = −1.5x2 + 250x − (80x + 150) = −1.5x2 + 170x − 150.
2. To ﬁnd the x-in...
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