I'm really in need of math help, because I'm failing! please?

Question

A golf company has determined that the daily per unit cost C of manufacturing x additional Big Bertha – type golf clubs may be expressed by the quadratic function

C(x) = 5x^2 – 620x + 20,000

a)How many clubs should be manufactured to minimize the additional cost per club?

b)At this level of production , what is the additional cost per club?

Answer 1

Hi,

For a quadratic equation like C(x) = 5x^2 – 620x + 20,000, the graph is a parabola opening up, so it has a minimum value at its vertex, which is on the axis of symmetry. The axis of symmetry is found by x = -b/(2a). In this case the axis is x = -(-620)/(2*5) = 620/10 = 62.

This means the minimum cost would occur by manufacturing 62 additional Big Bertha – type golf clubs. By plugging 62 into the formula, the minimum cost is 780. The cost per club for the additional production is $12.58.

I hope that helps!! :-)

Answer 2

The minimum of a quadratic function is always at the vertex. The fastest way to find the vertex of a quadratic equation is to take the derivative of the function.

C' = 10x - 620

The vertex is always where the slope (C') = 0

0 = 10x -620

620 = 10x

62 = x

So, the number of clubs to minimize the amount per club is 62. This is your answer for part a.

For part b, we simply need to plug in the number 62 for the number of clubs and find the cost.

C = 5 (62)^2 - 620 (62) + 20000 = 780

Therefore, the cost per club will be 780 / 62 = $12.58

Answer 3

You want to know the rate of change of the cost C with unit change in production.

Take the derivative:
dC/dx = 10x - 620

At an inflection point (i.e. at a maximum or a minimum, the derivative is zero, so
10x - 620 = 0

x = 62 clubs

The additional cost is $12.58 (just substitute x in your original equation to get the cost of the 62 clubs, and divide the result by 62.

Answer 4

a)
C(x) = 5x^2 – 620x + 20,000
C'(x) = 10x - 620
when C'(x) = 0 = 10x - 620
10x = 620
x=62
62 clubs should be produced.

b)C(62)= 5(62)^2 - 620(62) + 20000
=780
Additional cost per club = 780 / 62
=$12.6

Answer 5

From the quadratic equation you can use a derivative to find the vertex of the parabola.
-b/2(a)
-(-620) / 2(5)
620 / 10 = 62