Lian is a production analyst at the cardboard box manufacturer Flexpac. Last year, because of an increase in online shopping, shipping companies have increased the use of boxes for shipping. Management has charged Lian with generating a supply curve graph to illustrate the rise in price and supply of their boxes. These are the figures Lian discovered and put in a table. If you were assisting Lian, what steps would you tell her to take next?

  decide what sort of curve model is needed

Step-by-step explanation:

Lian's task is to generate a curve. The simplest way to do that is to graph the points and connect them with straight line segments. Lian will see that the curve has three different slopes.

The "curve" can be approximated by a linear function. Calculator or spreadsheet regression analysis will develop the curve ...

  q ≈ 1.64286p -53.2143

__

A slightly better curve fit can be obtained by using a cubic regression. That gives the relation ...

  q = 0.00001778p^3 -0.01295p^2 +4.465p -236.7

__

Lian needs to decide what sort of supply curve graph is required to satisfy the directive she has received.

it's

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)