Revenue, cost, demand, and profit

[fred2028]

So the question from my math book is:

The demand function for a new product is p(x)=-5x+21, where x represents the number of items in thousands and p represents the price in dollars. The cost function is C(x)=4x+14.
a) State the [...] revenue function.
b) Determine the [...] profit function.

I understand that the revenue function is unit price times quantity,

R(x)=(-5x+21)(x)

but when it comes to the profit (revenue-cost), how come the cost function C(x) isn't multiplied by the quantity?
I'm just one of those people that like to understand things inside-out before moving on

 

[tkhunny]

Notice how it is a UNIT revenue function. It is NOT a UNIT cost function. Some costs are fixed. The multiplication by number of units is in the cost function, multiplied by the marginal cost per unit. It's all in a very careful reading of the defintions.