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.Com
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) (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.
------------------------------------------------
(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
--------------------------------------------------------------------
(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:
RELATED QUESTIONS
18.
The revenue R received by a company selling x pairs of sunglasses per week is... (answered by josgarithmetic)
The total revenues (in dollars) for a company to sell x blank audiocassette tapes per... (answered by josmiceli)
A small manufacturing makes and sells x machines each month. The monthly cost, C ,in... (answered by CubeyThePenguin,ikleyn)
the total cost (in dollars) for a company to produce x items per week is C=7x+400. the... (answered by ikleyn)
The monthly revenue R achieved by selling x wristwatches is figured to be... (answered by Boreal)
The revenue R received for selling x stereos is given by the formula
R = −(x^2/3)... (answered by Alan3354)
The cost function for a certain company is
C = 30x + 600
and the revenue is given by
(answered by josgarithmetic,mananth)
A manufacturer finds that the revenue generated by selling x units of a certain commodity (answered by solver91311)
A manufacturer finds that the revenue generated by selling x units of a certain commodity (answered by edjones)