Help with demand functions that are linear equations?

Question

At a lemonade stand in NYC, the demand function for the number of glasses sold is:

 

x = 700 - 400p

 

where x is the number of glasses sold. The cost of running a lemonade stand has an initial cost of $200 plus an additional $.05 for each glass sold.

 

a) Find the revenue R as a function of x.

 

 

b)What is the marginal revenue function?

 

 

c) What is the marginal revenue when 200 glasses and 500 glasses are sold?

Answer 1

 

(A)

 

(700-x)/400 = p

 

R(x) = x(700-x)/400

 

 

(B) R'(x) = (-x  +  700 - x )/400

              = (-2x + 700)/400

 

(c) R'(200) = (-2*200 + 700)/400 = (-400+700)/400 = 300/400 = 3/4 = 0.75

 

    R'(500) = (-2*500 + 700)/400 = (-1000 + 700)/400 = -300/400 = -0.75