find the min cost

Question

A manufacturer of lighting fixtures has daily production costs of , where C is the total cost in dollars and  is the number of fixtures produced.

a. How many fixtures should be produced each day to yield a minimum cost?

 b. What is the minimum cost?

Answer 1

At the minimum or maximum of any equation, the derivative will equal 0. Find C'(x) and set it equal to 0. Solve for x. Then you have to check which x's are minima and which are maxima. You can sketch the graph since C(x) is a simple parabola, but I prefer to take the double derivative. Take the derivative of the derivative (so find C''(x)) and plug in your x's.

If C''(x) <0 , it is a local maximum

If C''(x) >0, it is a local minimum

If C''(x)=0, then the test failed and you would have to use other ways to find out.

For a in the question, x will be the number of fixtures.

For b, you just have to plug in your x to C(x) to find the minimum cost.

I hope this helps!