SOLUTION: A toy factory produces wooden puzzles that get sold in toy stores. The cost per puzzle, C (in dollars), to produce the puzzles, p (in hundreds) on any given day is modeled by the c

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A toy factory produces wooden puzzles that get sold in toy stores. The cost per puzzle, C (in dollars), to produce the puzzles, p (in hundreds) on any given day is modeled by the c      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1013609: A toy factory produces wooden puzzles that get sold in toy stores. The cost per puzzle, C (in dollars), to produce the puzzles, p (in hundreds) on any given day is modeled by the cost function below.
C= 0.006p (squared) - 0.036p + 0.7
Find the number of puzzles that the factory should make each day to minimize the cost per puzzle
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C+=+.006p%5E2+-+.036p+%2B+.7+
+C+ is plotted on the vertical axis
+p+ is plotted on the horizontal axis
You need to find the point ( C,p ) where
+C+ is a minimum
-------------------------------
The formula for +p+ when +C+ is a
minimum is:
+p%5Bmin%5D+=+-b%2F%282a%29+ when the equation
is in the form:
+C+=+a%2Ap%5E2+%2B+b%2Ap+%2B+c+
+a+=+.006+
+b+=+-.036+
---------------
+p%5Bmin%5D+=+-%28+-.036+%29+%2F+%28+2%2A.006+%29+
+p%5Bmin%5D+=+.036+%2F+.012+
+p%5Bmin%5D+=+3+
-----------------
making 3 puzzles/day will minimize
the cost/puzzle
--------------------
check:
Here's the plot:
+graph%28+400%2C+400%2C+-20%2C+60%2C+-10%2C+50%2C+.006x%5E2+-+.036x+%2B+.7+%29+
Answer could be right.
Plug +p+=+3.1+ and +p+=+2.9+ into the
equation and see if +C+ is NOT a minimum in each case