Help i need answers to maximizing and minimizing problems

[equis1989]

Homework Statement

JNK Inc. has asked you to perform an analysis of their widget manufacturing business. by completing a marketing survey, JNK inc. was able to determine that by selling their widgets for 4 dollars instead of 5 dollars they were able to sell 120 widgets instead of 100 widgets. currently the company pays 100 dollars to rent their gactory regardless of whether they make anything. in addition, it costs JNK inc. $1 to manufacture each widget.
-What is the price function for the companys widgets? the price function p(x) is the price that a company has to charge in order to sell x units.
-what is the maximum amount of revenue they can make?

Homework Equations

The Attempt at a Solution

p(x)=100+4X

 

[HallsofIvy]

p(x)= 100+4x says "they will sell x widgets if the price is p(x)= 100+ 4x dollars". In particular, that says, "they will sell 4 widgets if the price is p(x)= 100+ 16= 116 dollars". That is NOT what the problem says. You might notice one immediate difficulty: your price function is increasing. The MORE they charge, the MORE they sell! That obviously doesn't happen here. Since you have shown no work and not said HOW you got that function, I can't give any suggestions as to what you might have done wrong.

 

[equis1989]

I have been working on it, and i realized what i have done wrong. for the cost, i think the equations would be p(x)=4X and p(x)=5X, and the revenue equations would be p(x)=100+4x and p(x)=100+5X, from there i can get the maximum revenue...?

 

[HallsofIvy]

Again, that makes no sense- you have two different price functions!

You want a function of the form p(x)= Ax+ B such that p(100)= 5 and p(120)= 4.

p(100)= 100A+ B= 5 and p(120)= 120A+ B= 4. Solve those two equations for A and B.