Irons Graph

plz need help urgently?

The market research department of a company recommends that the company manufacture steam irons. After suitable test marketing, the research department presents the demand equation p = -0.3x + 300, where x is the number of irons retailers are likely to buy per week at $p per iron. The financial department provides the cost equation C(x) = 15,000 + 30x.

(a)Express revenue R(x) as a function of x and specify the domain.

(b)Graph R(x) and C(x) on the same coordinate system.

(c)Find the break even points

a) Revenue is just price * quantity. the quantity is x, and the price is p, and p=-0.3x + 300, so the revenue function is:

x * (-0.3x + 300) = R(x) = -0.3x² + 300x

the domain is every x above zero that satisfies that equation, so set it to zero to find the two points where the function crosses zero:

-300 ± √300²
-------------------
-.6

0
--- = 0
-.6

-600
------ = 1000
-.6

so the domain for R(x) = -0.3x² + 300x is (0,1000)

b) you'll need to do the graph!

c) set 15,000 + 30x = -.3x² + 300x

.3x² - 300x + 30x + 15000 = 0

.3x² - 270x + 15000 = 0

using (-(-270) ± √(-270)² -4(.3)(15000)) / 2,
we find two break even points,

x = 59.48752, and
x = 840.5125

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