Question 5766
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:
{{{x=(x/2)+125}}}
subtract {{{x/2}}} from both sides of the equation:
{{{x-(x/2)=125}}}
{{{(x/2) = 125}}}
multiply both sides by 2:
{{{x=250}}}
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.