SOLUTION: A food truck sells 60 hot dogs each day when it charges $4.00 per hot dog. For a $0.50 decrease in price, the food truck sells 10 more hot dogs. a. How much should the food tru

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A food truck sells 60 hot dogs each day when it charges $4.00 per hot dog. For a $0.50 decrease in price, the food truck sells 10 more hot dogs. a. How much should the food tru      Log On


   

Question 1051678: A food truck sells 60 hot dogs each day when it charges $4.00 per hot dog. For a $0.50 decrease in price, the food truck sells 10 more hot dogs.
a. How much should the food truck charge to maximize daily revenue?
The food truck should charge $__ per hot dog.
b. What is the maximum daily revenue?
The maximum daily revenue is $__.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of $.50 increases in price
Let +P+ = the price of +60+%2B+10n+ hot dogs
+P+=+%28+60+%2B+10n+%29%2A%28+4+-+.5n+%29+
+P+=+240+%2B+40n+-+30n+-+5n%5E2+
+P+=+-5n%5E2+%2B+10n+%2B+240+
The n-value of +P+ is
+n%5Bmax%5D+=++-b%2F%282a%29+
+n%5Bmax%5D+=+-10%2F%282%2A%28-5%29%29+
+n%5Bmax%5D+=+1+
--------------------
+n+=+1+
+P+=+%28+60+%2B+10%2A1+%29%2A%28+4+-+.5%2A1+%29+
+P+=+70%2A3.5+
+P+=+245+
--------------------------------
(a)
The food truck should charge $3.50 per hot dog
(b)
The maximum daily revenue is $245
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check:
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+10%2C+-30%2C+280%2C+-5x%5E2+%2B+10x+%2B+240+%29+