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Question 795092: The demand equation for a product is given by x=5000-5p, where x is the number of units produced and sold at price p(in dollars) per unit. The cost(in dollars) of producing x units is given by C(x)=4x+12,000. Express each of the following as a function of price.
a. Cost
b. Revenue
c. Profit
So I was doing my homework and I came across this problem and I honestly have no idea what it is asking for, and have no clue how to solve it. If you could please help me solve it I would really appreciate it.(It's the last problem I have to do on my homework) Thank You
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The demand equation for a product is given by x=5000-5p, where x is the number of units produced and sold at price p(in dollars) per unit.
The cost(in dollars) of producing x units is given by C(x)=4x+12,000.
Express each of the following as a function of price.
:
a. Cost
Cost equation is given as: C(x)=4x+12,000.
replace x with (5000-5p)
C(p) = 4(5000-5p)+ 12000
C(p) = 20000 - 20p + 12000
C(p) = -20p + 32000
:
b. Revenue
Rev = Units sold * price
R(p) = x * p
replace x with (5000-5p)
R(p) = p(5000-5p)
R(p) = -5p^2 + 5000p
:
c. Profit
P = Rev - Cost
P(p) = -5p^2 + 5000p - (-20p + 32000)
P(p) = -5p^2 + 5000p + 20p - 32000
P(p) = -5p^2 + 5020p - 32000
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