53.4k views
5 votes
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function c(x) = 0.3x^2 - 156x + 26,657 . How many machines must be made to minimize the unit cost?

Do not round your answer.

2 Answers

3 votes

Answer:

260 machines for minimum cost.

Explanation:

c(x) = 0.3x^2 - 156x + 26.657

Finding the derivative:

c'(x) = 0.6x - 156

0.6x - 156 = 0 for maxm/minm cost.

x = 156 / 0.6

= 260

The second derivative is positive (0.6) so this is a minimum.

User Dtengeri
by
8.6k points
3 votes

Answer:


x=260\ machines

Explanation:

Note that we have a cudratic function of negative principal coefficient.

The minimum value reached by this function is found in its vertex.

For a quadratic function of the form


ax ^ 2 + bx + c

the x coordinate of the vertex is given by the following expression


x=-(b)/(2a)

In this case the function is:


C(x) = 0.3x^2 - 156x + 26,657

So:


a=0.3\\b=-156\\c=26,657

Then the x coordinate of the vertex is:


x=-(-156)/(2(0.3))


x=260\ machines

Then the number of machines that must be made to minimize the cost is:


x=260\ machines

User AlienOnEarth
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories