SOLUTION: The revenue R received by a company selling x pairs of sunglasses per week is given by the function R(x) = -0.1x^2 + 30x. (a) Find the values of R(1212) and R(1515) How(b

Algebra ->  Finance -> SOLUTION: The revenue R received by a company selling x pairs of sunglasses per week is given by the function R(x) = -0.1x^2 + 30x. (a) Find the values of R(1212) and R(1515) How(b      Log On


   

Question 1080776: The revenue R received by a company selling x pairs of sunglasses per week is given by the function R(x) = -0.1x^2 + 30x.

(a) Find the values of R(1212) and R(1515)

How(b) How many pairs of sunglasses must be sold in order for the revenue to be $2000 per week?

(c) How many pairs of sunglasses must be sold in order for revenue to be $2250 per week?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i translated what you wrote to a simpler version as follows:

The revenue R received by a company selling x pairs of sunglasses per week is given by the function R(x) = -0.1x^2 + 30x.

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(a) Find the values of R(1212) and R(1515)

in order to find the values of R(1212) and R(1515), you just need to substitute the argument of x in R(x) = -.1x^2 + 30x, to these numbers.

you will get R(1212) = -.1 * (1212)^2 + 30 * 1212 = -110534.4

you will get R(1515) = -.1 * (1515)^2 + 30 * 1515 = -184072.5

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(b) How many pairs of sunglasses must be sold in order for the revenue to be $2000 per week?

to find this value, replace R(x) with 2000 and the formula becomes:

2000 = -.1* x^2 + 30 * x

add .1 * x^2 to both sides of the equation and subtract 30 * x from both sides of the equation to get:

.1 * x^2 - 30 * x + 2000 = 0

factor this quadratic equation to get:

x = 100 or x = 200

the revenue will be 2000 when either 100 pair of glasses are sold or 200 pair of glasses are sold.

(c) How many pairs of sunglasses must be sold in order for revenue to be $2250 per week?

the equation becomes 2250 = -.1 * x^2 + 30 * x

convert the equation to standard form as we did in part b to get:

.1 * x^2 - 30 * x + 2250 = 0

factor this quadratic equation to get:

x = 150

the revenue will be 2250 when 150 pairs of glasses are sold.

you can graph the equation and should be able to see all of these solutions.

the graph to show revenues of 2000 and 2250 is shown below:

$$$

the graph to show revenues caused by x = 1212 and x = 1515 are shown below:

$$$