SOLUTION: Susan makes and sells necklaces on a beach. When she sells the necklaces for Php 100 each, she sells an average of 20 necklaces per day. When she increases the price to Php 120, th

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Question 1144350: Susan makes and sells necklaces on a beach. When she sells the necklaces for Php 100 each, she sells an average of 20 necklaces per day. When she increases the price to Php 120, the average sales drop by two per day.
a. Find the demand as a function of price assuming that it is linear.
b. Find the revenue as a function of price.

Answer by ikleyn(52878)   (Show Source): You can put this solution on YOUR website!
.

(A)  When the price is Php 100 for necklace, she sells 120 necklaces.

     When the price is Php 120  for necklace, she sells 120-2 necklaces.


    The demand function  d(p) is the function, which says how many necklaces (d) is sold at a given price (p).


    So, in your case, the demand function takes the value of 120 (necklaces)  at the price of Php 100 and

    decreases by 2 when the price increases by Php 20.


    Since the function is assumed to be linear, it means that  d(p) = 120 - , or, equivalently,  d(p) = 120 - 0.1*(p-100).


    It is the ANSWER to question (A).


    CHECK it :  if p= 100, you have d(100) = 120 - 0.1*(100-100) = 120 - 0.1*0 = 120.                                 ! Precisely Correct !

                if p= 120, you have d(120) = 120 - 0.1*(120-100) = 120 - 0.1*20 = 120-2 = 118.    ! Drop by 2, which is PRECISELY Correct !



(B)  Question (B) is even easier (!)


     The revenue function is the product of the price for single unit to the number of units.

      In your case, the revenue function is the product of the price "p" by the number of units "d(p)", which represent the number of units.


      So, you have  R(p) = p*d(p) = p*(120 - 0.1*(p-100)).


      You just have the revenue function R(p) as the function of price "p", expressed in this way.


      You can simplify it:
 

          R(p) = 120p - 0.1*p^2 + 10p = -0.1*p^2 + 130p.


      It is your final ANSWER to question (B).


      Notice, that the demand function d(p) is a linear function of the argument "p".

                   The revenue function R(p) is a quadratic function of price "p".

You have the solution completed and fully explained.

I explained it in such a detailed way, since I assume that you are a beginner in this area and solve such a problem
for the first time in your life.

When you learn on how to solve such problems, you will be able to do it in 2 lines.


Happy learning (!)


In this site, there is a lesson which shows and teaches students on how to solve relevant problems of "real life".


Come again to this forum soon to learn more (!)



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