Chapter 6.5, Problem 35PPE

To determine

To calculatenumber of refrigerators and number of pianos the truck could carry. write and graph an inequality also find can 12 refrigerators and 8 pianos overload the truck.Write an inequality symbol used. State the side of boundary lines that should be shaded.

Answer to Problem 35PPE

  $250x+475y\le 6400$

  

the truck will overload.

less or equal to inequality is used here.

Origin side should be shaded.

Explanation of Solution

Given information:A truck that can carry no more than $6400$ lb. is being used to transport refrigerators and upright pianos. Each refrigerator weighs $250$ lb. and each piano weigh $475$

lb. Calculation:

Let’s first formulate equations for given situations,

Let’s say you choose to transport $x$ refrigerators and $y$ pianos.

Now, truck that can carry no more than $6400$ lb., Each refrigerator weighs $250$ lb. and each piano weigh $475$ lb.

  $\therefore 250x+475y\le 6400$

Let’s plot this inequality,

  

Red area is a common area of solution.

If $x$ and $y$ follows the inequality below, the truck will not overload.

  $250x+475y\le 6400$

Here, $x=12,y=8$

  $\therefore 3000+3800\le 6400$

  $\therefore 6800\le 6400$ which is not true

Therefore, the truck will overload.

As the truck can bear maximum $6400$ lb., it can fill with less than or equal to $6400$ lb .So less or equal to inequality is used here. As origin follows the inequality of system. The portion which contains origin should be shaded.