The cost to produce one compact disc is $1.75 plus a one-time fixed cost of $3000 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=
The formula that gives the cost C of producing x compact discs is:
C = 1.75x + 3000
(b) Write a formula that gives the revenue R from selling x compact discs
The formula that gives the revenue R from selling x compact discs is:
R = 13x
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
The formula that calculates the profit P from selling x compact discs is:
P = R - C
Substituting the formulas for revenue and cost:
P = 13x - (1.75x + 3000)
Simplifying:
P = 11.25x - 3000
(d) How many compact discs need to be sold to yield a positive profit?
To find how many compact discs need to be sold to yield a positive profit, we need to set the profit formula equal to zero and solve for x:
11.25x - 3000 = 0
Adding 3000 to both sides:
11.25x = 3000
Dividing both sides by 11.25:
x = 3000 / 11.25
x ≈ 266.67
Since we cannot sell a fraction of a compact disc, we round up to the nearest whole number. Therefore, we need to sell at least 267 compact discs to yield a positive profit.