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.)
11.25x - 2900 > 0
11.25x > 2900
x > 2900/11.25
x > 258.22
Therefore, 259 or more compact discs should be sold to yield a positive profit.
To yield a positive profit, we need to find the value of x where P is greater than 0.
P = 11.25x - 2900
Setting P greater than 0, we get:
11.25x - 2900 > 0
11.25x > 2900
x > 2900 / 11.25
x > 257.777
Since x represents the number of compact discs, we round up to the nearest whole number.
Therefore, 258 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
Now, let's solve for x:
11.25x > 2900
Divide both sides of the inequality by 11.25:
x > 2900 / 11.25
Simplifying the right side of the inequality:
x > 256.88
So, we need to sell more than 256.88 compact discs to yield a positive profit.
Since we cannot sell a fraction of a compact disc, we round up to the nearest whole number. Therefore, we need to sell 257 or more compact discs to yield a positive profit.