SOLUTION: If a manufacturer charges p dollars each for rugby shirts, then he expects to sell 2000 - 100p shirts per week. What polynomial represents the total revenue expected for a week? Ho

Question 143366: If a manufacturer charges p dollars each for rugby shirts, then he expects to sell 2000 - 100p shirts per week. What polynomial represents the total revenue expected for a week? How many shirts will be sold if the manufacturer charges $20 each for the shirts? Find the total revenue when the shirts are sold for $20 each.
So far what I have come up with is P(R) = 2000 - 100p, but I really don't think it is correct. I just don't seem to find enough facts to put together an equation - can you please help? Thanks!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You are looking for total revenue, R, as a function of price. Total revenue is the number of items sold times the price of each. It just so happens in this case that the number of items sold, N, is itself a function of the price.

N(p) is given: and we have defined R(p) as , or

Notice that at $20, the number of shirts sold, according to the given quantity sold model, is zero, hence the revenue will also be zero. It would seem that is a rather poor real-world model for the relationship between price and number sold for rugby shirts which typically range in the $30 to $50 range, though I have seen some fetching $120 and up.
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