5.6 Graphing systems of linear inequalities  (Page 4/10)

Solution

ⓐ Let $h=$ the number of hamburgers.
$c=$ the number of cookies
To find the system of inequalities, translate the information.
The calories from hamburgers at 240 calories each, plus the calories from cookies at 160 calories each must be more that 800.

The amount spent on hamburgers at $1.40 each, plus the amount spent on cookies at $0.50 each must be no more than $5.00.

We have our system of inequalities. $\{\begin{array}{c}240h+160c\ge 800\hfill \\ 1.40h+0.50c\le 5\hfill \end{array}$

ⓑ

To graph $240h+160c\ge 800$ graph $240h+160c=800$ as a solid line. Choose (0, 0) as a test point. it does not make the inequality true. So, shade (red) the side that does not include the point (0, 0). To graph $1.40h+0.50c\le 5$ , graph $1.40h+0.50c=5$ as a solid line. Choose (0,0) as a test point. It makes the inequality true. So, shade (blue) the side that includes the point.

ⓒ To determine if 3 hamburgers and 2 cookies would meet Omar’s criteria, we see if the point (3, 2) is in the solution region. It is. He might choose to eat 3 hamburgers and 2 cookies.
ⓓ To determine if 2 hamburgers and 4 cookies would meet Omar’s criteria, we see if the point (2, 4) is in the solution region. It is not. Omar would not choose to eat 2 hamburgers and 4 cookies.

We could also test the possible solutions by substituting the values into each inequality.