Question

Your boss and see the monthly data that shows the number of orders coming into and out of the warehouse. The data is in the table below. Explain to your boss, in complete sentences, the solution to the system and what the solution represents.(January 1) 3, 3 out (February 2) 6, 4out (March 3) 9, 5out (april 4) 12, 6out

Answer 1

You have the next table of values:

As you can see in the table, the No. of orders coming in increases by 3 each month. Also the number of orders coming out, increases by 1 each month. Then, you can find the function that represents the data, since it is a line, as follows:

The general equation of a line is given by:

`y=mx+b`

Where m is the slope and b the y-intercept.

You can find the slope by using the next formula:

`m=(y2-y1)/(x2-x1)`

Let's use the next two points (3, 3) and (12, 6):

`m=(6-3)/(12-3)=(3)/(9)=(1)/(3)`

You can also find the intercept as:

`\begin{gathered} y=(1)/(3)x+b \\ 3=(1)/(3)3+b \\ 3=1+b \\ 3-1=b \\ b=2 \end{gathered}`

Then, the general equation of the line is:

`y=(1)/(3)x+2`

The value of the slope means that for every 3 units that the x-variable increases (the No. of orders coming into the warehouse) the y-variable increases by 1 unit (the No. of orders coming out of the warehouse).

Then, you need to explain to your boss that when the number of orders coming into the warehouse is greater than 3, the number of orders coming out won't be equal to that value. For every 3 extra orders coming in, the warehouse is only available to send out 1. Thus, when are accepted more than 3 orders, the warehouse has not the capability to respond to these orders.