SOLUTION: Hello, Do I need to rearange this type problem to solve? Please advise.... Thanks. Q 19: A company uses the cost function C (w) = 0.04 w^2 � 6.0 w + 275 to model the un

Question 60372This question is from textbook Elementry and Intermediate Algebra
: Hello,
Do I need to rearange this type problem to solve?
Please advise....
Thanks.
Q 19: A company uses the cost function C (w) = 0.04 w^2 � 6.0 w + 275 to model the unit cost in dollars for producing �w� widgets. Find:
a. How many widgets the company needs to make to achieve minimum unit cost?
b. What is the minimum unit cost? This question is from textbook Elementry and Intermediate Algebra

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You can plot this equation or just picture what it should look like
I'll just try to describe it.
(1) Because the term is positive, the graph is a parabola
that slopes negatively down from the left, comes down to a minimum and
slopes back up positively.
(2) The problem is to find the minimum. The minimum will be half way
between two values of w that have the same C(w), in other words, half
way between the points (w[1],C[1]) and (w[2],C[2]) where C[1] = C[2]

If they don't produce any widgets, the fixed cost is $275

Now, if I find another value of w for which C(w) = 275, the C(w) mid-
way between (0,275) and (w[2],275) will be minimum cost

subtract 275 from both sides

If the 1st factor, w, is zero, that's the point we already have, (0,275)
so, set the 2nd factor equal to zero.

That's our 2nd point. We now have (0,275 and (150,275)
The minimum C is halfway between the w's, or
That's the answer to (a), 75 widgets made give minimum cost
Now find C(w)

That means the min is at (75,50) and the answer to (b) is
the minimum unit cost is $50
A simple test will tell you if this is truly the min
Find C(w) for w = 74.9 and for w= 75.1. These values of w should
give costs that are both slightly higher than $50.
I get C(w) = 50.0004 for both
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