SOLUTION: A food truck sells 100 hot dogs each day when it charges $2.00 per hot dog. For a $0.25 decrease in price, the food truck sells 25 more hot dogs. a. How much should the food tr

Question 1120089: A food truck sells 100 hot dogs each day when it charges $2.00 per hot dog. For a $0.25 decrease in price, the food truck sells 25 more hot dogs.
a. How much should the food truck charge to maximize daily revenue?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

An equivalent rephrasing is  "for each decrease the price in 1 cent the number of sold hot dogs increases in 1", or

in the Math term, at the price  200-n  cents  the number of sold hot dogs is 100+n.


Then the revenue is  R(n) = (100+n)*(200-n) = 20000 + 200n - 100n - n^2 = -n^2 + 100n + 20000.


And the problem asks to find the maximum of the quadratic form  R(n).


The maximum is achieved at  n =  = 50.


Anser.  The food truck should charge 200-50 = 150 cents = $1.50 per hot dog.

My lessons in this site on finding the maximum/minimum of a quadratic function are
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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