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.

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Аноним Аноним · Answer 1 · 2019-07-05T20:53:01+02:00

Answer:

260 machines for minimum cost.

Step-by-step 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.

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luisejr77 luisejr77 · Answer 2 · 2019-07-05T21:57:43+02:00

Answer:

[tex]x=260\ machines[/tex]

Step-by-step 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

[tex]ax ^ 2 + bx + c[/tex]

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

[tex]x=-\frac{b}{2a}[/tex]

In this case the function is:

[tex]C(x) = 0.3x^2 - 156x + 26,657[/tex]

So:

[tex]a=0.3\\b=-156\\c=26,657[/tex]

Then the x coordinate of the vertex is:

[tex]x=-\frac{-156}{2(0.3)}[/tex]

[tex]x=260\ machines[/tex]

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

[tex]x=260\ machines[/tex]