Chapter 6.6, Problem 38PPE

To determine

To determine and graph the system of inequality.

Explanation of Solution

Given:

Student artwork is 20 feet long

Some pieces are 8.5 inch wide

Other pieces are 11 inch wide

Leave 3 inch of space to the left of each art piece

Post at least 16 pieces of art

Calculation:

Let $x$ be number of $8.5$ inch in wide paintings and $y$ be number of $11$ inch painting,

  $\Rightarrow x+y\ge 16$

Now, $20$ feet $=240$ inch

Need to leave 3 inch of space to the left of each art piece.

So, adding 3 to the width of the painting

  $\Rightarrow 11.5x+14y\le 240$

Inequality I: $y\ge -x+16$

Here, the slope is $-1$ and $y$ intercept is $16$ .

Inequality II: $y\le -\frac{23}{28}x+\frac{120}{7}$

Here, the slope is $-\frac{23}{28}$ and $y$ intercept is $\frac{120}{7}$ .

Graph:

  

Here $x$ and $y$ are always positive. The green dark region with black boundaries represents the solution of system of inequality.

Interpretation:

Therefore, the dark green shaded region is the solution of the system of inequation.