SOLUTION: The vending machine on the fourth floor of your building sells bottles of soft drink at a price of $1 per bottle. Let X denote the number of bottles of soft drink sold each week.

Question 5766: The vending machine on the fourth floor of your building sells bottles of soft drink at a price of $1 per bottle. Let X denote the number of bottles of soft drink sold each week.
A) What is the revenue function: R(x) = ?
B) If the fixed cost for the owner of this vending machine is $125 per week, and the wholesale cost of each bottle is 50 cents, what is the total cost function: C(x) = ?
C) What is the profit function: P(x) = ?
D) What is the Break- Even Point: BEP = ?
Answer by Abbey(339) (Show Source): You can put this solution on YOUR website!
Let x = the number of bottles sold
Revenue will equal $1 multiplied by the number of bottles sold,
R(x)=$1(x)
The fixed cost for the owner is $125 and the wholesale cost is 50 cents.
To create the cost function C(x), multiply the number of bottles sold by 50 cents and add $125 to the total:
C(x) = $.50(x) + $125
The profit function is the revenue function - the cost function:
P(x)=$1(x)-($.50(x)+$125)
Finally, the break even point will be when the revenue is equal to the cost:
$1x=$.50(x)+$125
convert the dollars and cents into fractions and integers:

subtract from both sides of the equation:

multiply both sides by 2:

so the break even point occurs when 250 cans of soft drinks have been sold.

This makes sense because if the machine sells 250 cans of soda, it has earned $250. the cost of 250 cans is $125 + the fixed cost of $125 = $250.

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