The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P=
enter your response here (Simplify your answer.)
5 answers
P = (12x) - (1.75x + 2400)
The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
Question content area bottom
Part 1
(a) Write a formula that gives the cost C of producing x compact discs. Be sure to include the fixed cost.
C
=
1.75 x plus 2400
1.75x+2400 (Simplify your answer.)
Part 2
(b) Write a formula that gives the revenue R from selling x compact discs.
R
=
12 x
12x (Simplify your answer.)
Part 3
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P
=
10.25 x minus 2400
10.25x−2400 (Simplify your answer.)
Part 4
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
Question content area bottom
Part 1
(a) Write a formula that gives the cost C of producing x compact discs. Be sure to include the fixed cost.
C
=
1.75 x plus 2400
1.75x+2400 (Simplify your answer.)
Part 2
(b) Write a formula that gives the revenue R from selling x compact discs.
R
=
12 x
12x (Simplify your answer.)
Part 3
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P
=
10.25 x minus 2400
10.25x−2400 (Simplify your answer.)
Part 4
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
Part 4:
To yield a positive profit, the formula for profit (P) should be greater than zero:
10.25x - 2400 > 0
Solving this inequality, we have:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs should be sold to yield a positive profit.
To yield a positive profit, the formula for profit (P) should be greater than zero:
10.25x - 2400 > 0
Solving this inequality, we have:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs should be sold to yield a positive profit.
The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
To calculate the number of compact discs that need to be sold to yield a positive profit, we can set the profit equation (P) to be greater than zero:
P > 0
Substituting the given values, the profit equation is:
(12x) - (1.75x + 2400) > 0
Simplifying the equation:
12x - 1.75x - 2400 > 0
10.25x - 2400 > 0
To solve for x, we isolate the variable:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs need to be sold to yield a positive profit.
P > 0
Substituting the given values, the profit equation is:
(12x) - (1.75x + 2400) > 0
Simplifying the equation:
12x - 1.75x - 2400 > 0
10.25x - 2400 > 0
To solve for x, we isolate the variable:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs need to be sold to yield a positive profit.