SOLUTION: The manufacturer of an energy drink spends $1.50 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $5,000. (a) Find the cost function

Question 1191394: The manufacturer of an energy drink spends $1.50 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $5,000.
(a)
Find the cost function C when x energy drinks are manufactured.
C(x) =

(b)
Find the revenue function R when x drinks are sold.
R(x) =

(c)
Show the break-even point by graphing both the revenue and cost functions on the same grid. (Plot each function as a line, not a ray.)
(d)
Find the break-even point. Interpret what the break-even point means.
When___energy drinks are sold, the cost and revenue equal $___.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c(x) = 5000 + 1.5 * x
r(x) = 2 * x
break even when r(x) = c(x)
this means:
5000 + 1.5 * x = 2 * x
subtract 1.5 * x from both sides of this equation to get:
5000 = .5 * x
solve for x to get:
x = 5000 / .5 = 10,000
break even is when x = 10,000 drinks are made and sold.
when x = 10,000:
c(x) = 5000 + 1.5 * 10,000 = 20,000
r(x) = 2 * 10,000 = 20,000
revenue equals cost.
that's the break even point.
there is no profit and no loss.
make and sell more than 10,000 units each month and you have a profit.
make and sell less than 10,000 units each month and you have a loss.

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