Chapter 5.6, Problem 39E

(a)

To determine

To write and graph: The inequality that represents the numbers of large and small boxes.

Answer to Problem 39E

  $\begin{array}{l}75x+40y+200\le 2000\text{or}\\ 75x+40y\le 1800\end{array}$

Explanation of Solution

Given information:

The number of large and small boxes a 200 pound delivery person that can take on the elevator.

Calculation:

Let,

  $\begin{array}{l}x\to \text{number}\text{of}\text{large}\text{}\text{box}\\ y\to \text{number}\text{of}\text{small}\text{}\text{box}\end{array}$

The weight limit will be at most 2000 lb including the weight of the delivery person so the inequality will be:

  $\begin{array}{l}75x+40y+200\le 2000\text{or}\\ 75x+40y\le 1800\end{array}$

Graph $75x+40y=1800\text{or }y=-1.875x+45$

Use a solid line because the inequality symbol is $\le$ . Restrict the graph to positive x & y values since negative values do not make sense in this real-life context.

  $\begin{array}{l}\text{Test}\left(0,0\right):\\ 75\left(0\right)+40\left(0\right)\le 1800\\ 0\le 1800\end{array}$

Because (0, 0) is a solution, shade the half-plane that contains (0, 0).

  

Conclusion:

The (0, 0) is a solution, shade the half-plane that contains (0, 0).

(b)

To determine

To explain: The reason for which the solutions of the inequality might not be practical in real life.

Explanation of Solution

Although the weight limit is not reached, some solutions are not practical such as (20, 5) which corresponds to 20 large boxes & 5 small boxes as such number of boxes won't fit in the elevator considering the sizes.