Question 190488: 86).Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 - 100p shirts at a tournament.
a) Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each.
b) Find R(5), R(10), and R(20).
c) Use the bar graph to determine the price that will give the maximum total revenue.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Revenue is the number of items sold times the price for each, so:
 = \left(2000-100p\right)p=2000p - 100p^2)
To find the value of any R(a), just substitute a for the independent variable, p in this case, and then do the arithmetic.
R(5):
\ =\ 2000(5) - 100(5)^2)
You can do your own arithmetic. And the other two are done exactly the same way.
I can't do a bar graph on this site, at least not without a great deal of work. You could put your data into Excel and have Excel create a chart for you.
There is a better way to find the price that gives the maximum revenue. Since the coefficient on the high order term is negative and this is a quadratic function, you know the graph of the function is a parabola opening downward. Hence, the vertex of the parabola is a maximum point. The value of the independent variable coordinate of the vertex of a parabola, and hence value of the independent variable that causes the function to be extreme, for a parabola of the form:
 = ax^2 + bx + c)
is given by:
For your function:
} = 10)
Meaning R(10) will give the largest R for any possible value of p
Super-double-plus extra credit:
What is the domain of this function? That is, what is the set of values that p could reasonably be?
John
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