SOLUTION: If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament. Find a polynomial R(p) that represents the total revenue when the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament. Find a polynomial R(p) that represents the total revenue when the      Log On


   

Question 190669: If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament.
Find a polynomial R(p) that represents the total revenue
when the shirts are p dollars each.
Find R(5), R(10), and R(20).
So far I have R=(2000-100)P(2000-100^2)
then I'm lost after that.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the revenue is simply the money that a individual/company has made BEFORE any expenses or taxes are accounted for. So this amount of money is solely determined by the amount of products/services that have been sold.


So basically, the revenue is

Revenue = (Price Per Product) x (Number of Products Sold)


In this case, since "a vendor charges p dollars each for rugby shirts", this means that the price is simply "p" and because "he expects to sell 2000-100p", this means that the number of products sold is 2000-100p


So just multiply the price by the quantity to get

R%28p%29=p%282000-100p%29


R%28p%29=2000p-100p%5E2 Distribute


R%28p%29=-100p%5E2%2B2000p Rearrange the terms.


So the polynomial that represents the revenue is R%28p%29=-100p%5E2%2B2000p

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Find R(5):


R%28p%29=-100p%5E2%2B2000p Start with the given equation.


R%285%29=-100%285%29%5E2%2B2000%285%29 Plug in p=5.


R%285%29=-100%2825%29%2B2000%285%29 Square 5 to get 25.


R%285%29=-2500%2B2000%285%29 Multiply -100 and 25 to get -2500.


R%285%29=-2500%2B10000 Multiply 2000 and 5 to get 10000.


R%285%29=7500 Combine like terms.


So this means that if the price is $5 a shirt, then he'll expect to make $7,500


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Find R(10):


R%28p%29=-100p%5E2%2B2000p Start with the given equation.


R%2810%29=-100%2810%29%5E2%2B2000%2810%29 Plug in p=10.


R%2810%29=-100%28100%29%2B2000%2810%29 Square 10 to get 100.


R%2810%29=-10000%2B2000%2810%29 Multiply -100 and 100 to get -10000.


R%2810%29=-10000%2B20000 Multiply 2000 and 10 to get 20000.


R%2810%29=10000 Combine like terms.



So this means that if the price is $10 a shirt, then he'll expect to make $10,000

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Find R(20):


R%28p%29=-100p%5E2%2B2000p Start with the given equation.


R%2820%29=-100%2820%29%5E2%2B2000%2820%29 Plug in p=20.


R%2820%29=-100%28400%29%2B2000%2820%29 Square 20 to get 400.


R%2820%29=-40000%2B2000%2820%29 Multiply -100 and 400 to get -40000.


R%2820%29=-40000%2B40000 Multiply 2000 and 20 to get 40000.


R%2820%29=0 Combine like terms.


So if the price is $20 per shirt, then he'll break even (he will neither gain or lose money).