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Question 1168738: A company produces very unusual cd’s for which the variable cost is $17 per CD and the fixed cost are $35000. They will sell the cd’s for $49 each. Let x be the number of cd’s produced. Write the total cost C as a function of the number of cd’s produced.
C=$_______
Write the total revenue R as a function of the number of cd’s produced.
R=$_______
Write the total profit P as a function of the number of cd’s produced
P=$___________
Find the number of cd’s which must be produced to break even.
The number of cd’s in which must be produced to break even is __________
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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