Question 1168738
let x = the number of CD's.


your cost function is:


C = 35000 + 17*x


35000 is the fixed cost.
17*x is the variable cost.


the fixed cost is the same regardless of how many CD's are sold.
the variable cost is the additional cost for each CD that is produced.
x represents the number of CD's that are produced.




your revenue function is:


R = 49*x


it is a variable cost only.
it represents the revenue received for each CD that is sold.
x represents the number of CD's that are sold.


the built in assumption of the problem is that the number of CD's sold is the same as the number of CD's produced.


that's why x represents the number of CD's in both the cost function and the revenue function.


your profit function is:


P = (49 * x) - (35000 + 17 * x).


P represents the profit.


(49 * x) represents the revenue.


(35000 + 17 * x) represents the cost.


profit is equal to revenue minus cost.


the equation reflects that.


to break even, the profit must be equal to 0.


if the profit was positive, you made mooney.
if the profit was negative, you lost money.
when the profit is 0, you didn't make money and you didn't lose money.
you just broke even.
that's why it's called the break even point.


to find how many CD's needed to be produced and sold to break even, set the profit equation equal to 0.


your profit equation of P = 49 * x - (35000 + 17 * x) becomes:


0 = 49 * x - (35000 + 17 * x)


simplify the equation by removing the parentheses to get:


0 = 49 * x - 35000 - 17 * x


combine like terms to get:


0 = 32 * x - 35000


add 35000 to both sides of the equation to get:


35000 = 32 * x


divide both sides of the equation by 32 to get:


35000 / 32 = x


solve for x to get:


x = 35000 / 32 = 1093.75


the number of CD's that must be produced and sold to break even is 1093.75


if you are still confused by any of this, let me know which part confuses you and i'll work to clear up the confusion as best i can.


theo