Consider the following functions that represent cost and revenue for the band's sales of spirit mugs.

f (x) = 100+3x

g (x) = 8x

a. Which function represents the cost function?

b. Which function represents the revenue function?

c. How can the functions be combined to create profit function?

d. Write the profit function.

Answer (a):

We have been given two functions f (x) = 100+3x and g (x) = 8x.

Now we need to decide which one of them is cost function and which one is the revenue function.

We know that production usually involves fixed cost for operating the production so usually that is of the form y=mx+b.

Hence f (x) = 100+3x is the cost function

Answer (b):

Then g (x) = 8x is the revenue function.

Answer (c):

We know that profit function is the difference of revenue and cost

Profit = Revenue - Cost

P (x) = g (x) - f (x) = 8x - (100+3x)

P (x) = 8x-100-3x

P (x) = 5x-100

Hence P (x) = 5x-100 is the profit function.

Answer (d):

P (x) = 5x-100 is the profit function.