**Unformatted text preview: **s the
3, 3
line x = 170 . To sketch a reasonable graph, we approximate the x-intercepts, (0.89, 0) and
3
(112.44, 0), and the vertex, (56.67, 4666.67). (Note that in order to get the x-intercepts and
the vertex to show up in the same picture, we had to scale the x-axis diﬀerently than the
y -axis. This results in the left-hand x-intercept and the y -intercept being uncomfortably close
to each other and to the origin in the picture.)
y
4000
3000
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1000 10 20 30 40 50 60 70 80 90 100 110 120 x 3. The zeros of P are the solutions to P (x) = 0, which we have found to be approximately
0.89 and 112.44. Since P represents the weekly proﬁt, P (x) = 0 means the weekly proﬁt
is $0. Sometimes, these values of x are called the ‘break-even’ points of the proﬁt function,
since these are places where the revenue equals the cost; in other words we gave sold enough
product to recover the cost spent to make the product. More importantly, we see from the
graph that as long as x is between 0.89 and 112.44,...

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