Graphing inequalities

Question

An online electronic store must sell at least 2,500 dollars worth of printers and computers per day. Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items per day. On a set of axes, Graph a system of inequalities that model these constraints.

Answer 1

Trisha,

 

The two inequalities that represent the situation are:

 

(1) at least $2500 worth of equipment must be sold every day and

(2) the store can ship a maximum of 15 total units each day

 

Let x be the number of printers and y be the number of computers.

 

Then, for eq1 we have:

 

$50x + $500y ≥ $2500 

 

For eq2:

 

x + y ≤ 15

 

Now, put each equation into the form y ≤ mx + b (or ≥; slope-intercept form of a linear equation)

 

For eq1, divide each term first by 50 to get:

 

x + 10y ≥ 50 or

 

10y ≥ -x + 50

 

10y/10 ≥ -x/10 + 5

 

y ≥ (-1/10)x + 25 (which is in the slope-intercept form)

 

For eq2:

 

x + y ≤ 15

 

y ≤ -x + 15 (again, in slope-intercept form)

 

When you graph inequalities, the region of interest lies to one side of the line or the other (including the line if it's ≥ or ≤).  When you graph these two inequalities (I assume you can do that), you will look for (x, y) pairs that satisfy both.  You can shade in the area where such points exist.

 

I hope this makes sense.