An ice cream shop costs $3000 per month for rent/utilities plus $2 per sco0op of ice cream. So their cost function can be written C(x) = 2x + 3000, where C is measured in terms of dollars and x is the number of scoops sold. 4x, where R is They sell the scoops for $4 each, so their revenue function is R(x) again measured in dollars and x is the number of scoops sold. CO R(x)- 4X a. Find their profit function P (x). (Hint: Profit is revenue minus cost.) c (x) 2x+ 3000 $ 30004Re month Pe scoop 2 C (x) 2x+3000 Cx)= 26)+3000 2X+ 30 p0 = 335 b. How many scoops do they have to sell in a month just to break even? (Hint: set P(x) 0 and solve for x.)

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Chapter7: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 29PT: For the following exercises, solve using a system of linear equations. 29. A factory producing cell...
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An ice cream shop costs $3000 per month for rent/utilities plus $2 per sco0op of ice
cream. So their cost function can be written C(x) = 2x + 3000, where C is measured in
terms of dollars and x is the number of scoops sold.
4x, where R is
They sell the scoops for $4 each, so their revenue function is R(x)
again measured in dollars and x is the number of scoops sold.
CO
R(x)- 4X
a. Find their profit function P (x). (Hint: Profit is revenue minus cost.)
c (x)
2x+ 3000
$ 30004Re month
Pe scoop
2
C (x) 2x+3000
Cx)= 26)+3000
2X+ 30 p0
= 335
b. How many scoops do they have to sell in a month just to break even? (Hint:
set P(x) 0 and solve for x.)
Transcribed Image Text:An ice cream shop costs $3000 per month for rent/utilities plus $2 per sco0op of ice cream. So their cost function can be written C(x) = 2x + 3000, where C is measured in terms of dollars and x is the number of scoops sold. 4x, where R is They sell the scoops for $4 each, so their revenue function is R(x) again measured in dollars and x is the number of scoops sold. CO R(x)- 4X a. Find their profit function P (x). (Hint: Profit is revenue minus cost.) c (x) 2x+ 3000 $ 30004Re month Pe scoop 2 C (x) 2x+3000 Cx)= 26)+3000 2X+ 30 p0 = 335 b. How many scoops do they have to sell in a month just to break even? (Hint: set P(x) 0 and solve for x.)
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