PLEASE SHOW ALL STEPS AND WORK FOR EACH ANSWER! PLEASE ALSO NOTE THAT THIS IS ON

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PLEASE SHOW ALL STEPS AND WORK FOR EACH ANSWER! PLEASE ALSO NOTE THAT THIS IS ONE QUESTION WITH 3 DIFFERENT PARTS. DO NOT ANSWER THE QUESTION IF YOU DO NOT KNOW HOW TO DO THE WORK OR EXPLAIN ALL OF THEM! THANK YOU!

A firm has total revenues given by R(X) = 18x - 0.01x^2 dollars for selling x units of a product. Use this information to answer the following questions. (a) How many units should be sold to maximize the revenue? Justify your answer. (b) What is the largest possible revenue that the firm can make? (c) Find the maximum revenue if production is limited to 750 units of product. Explain your answer.

Explanation / Answer

R(x) = 18x - 0.01x2

a) For revenue to be maximum. R'(x) = 0. Hence,
R'(x) = 18 - 0.02x = 0 => x = 900 units

b) Largest possible revenue can be made when units sold = 900. i.e x = 900.
R(x) = 18*900 - 0.01*9002 = $16119

c) R'(x) = 18 - 0.02x
R'(x) > 0 when 18 - 0.02x > 0 => 900 > x
Hence, for x < 900. R'(x) >0. Therefore, R(x) is increasing function till 900.
For x = 750. Maximum revenue will be at x = 750.
R(750) = 18*750 - 0.01*7502 = $13443.75

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