SOLUTION: The relationship between the number of units sold of a certain product, x, and the price obtained, p, is: x = 100-2p a) Find an expression for the total revenue for selling

Question 1028198: The relationship between the number of units sold of a certain product, x, and the price
obtained, p, is:
x = 100-2p
a) Find an expression for the total revenue for selling x units of the product.
b) How many units must be sold for the marginal revenue to be 25?
The total cost of producing x units of the product is:
TC (x)=0.5x^2+10x+100
c) Find an expression for the profit when producing and selling x units of the product.
d) How many units must be produced and sold to obtain maximum profit?
e) What is the maximum profit?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
x = 100 - 2p ==>
a) Revenue =
b) Marginal revenue is R'(x) = -x + 50.
==> -x + 50 = 25 ==> -x = -25 ==> x = 25 units must be sold for the marginal revenue to be 25.
c) Profit =.

d) Maximum number of units is obtained from units.
e) maximum profit = .
Thus the maximum profit is $300.

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