The cost to produce one compact disc is $1.75 plus a one-time fixed cost of $2900. The revenue received from selling one compact disc is $13.
(a) Write a formula that gives the cost C of producing x compact discs. Be sure to include the fixed cost.
C = 1.75x + 2900 (Simplify your answer.)
(b) Write a formula that gives the revenue R from selling x compact discs.
R= boxed 13x (Simplify your answer.)
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P = 11.25x - 2900 (Simplify your answer.)
(d) How many compact discs need to be sold to yield a positive profit?
__ or more compact discs should be sold. (Simplify your answer.)
To yield a positive profit, the revenue needs to be greater than the cost.
Let's use the profit formula P = 11.25x - 2900.
To find the number of compact discs that need to be sold to yield a positive profit, we need to solve the equation P > 0.
11.25x - 2900 > 0
To solve for x, we can isolate x on one side of the inequality:
11.25x > 2900
Divide both sides of the inequality by 11.25:
x > 2900 / 11.25
x > 256
Therefore, 257 or more compact discs should be sold to yield a positive profit.
To find the number of compact discs that need to be sold to yield a positive profit, we need to set the profit formula (P=11.25x-2900) greater than zero and solve for x.
11.25x - 2900 > 0
To solve this inequality, we need to isolate x.
11.25x > 2900
Divide both sides of the inequality by 11.25 to solve for x.
x > 2900/11.25
Using a calculator to evaluate 2900 divided by 11.25, we find:
x > 257.78
Since we can't sell a fraction of a compact disc, we need to round up to the nearest whole number. Therefore, 258 or more compact discs should be sold to yield a positive profit.