Chapter 11, Problem 104RE

a.

To determine

Write a system of linear inequalities that described the possible number of each kind of package.

Answer to Problem 104RE

  $\boxed{=0.75x+0.375y\le 120}$ , $\boxed{=0.5x+0.375y\le 72}$

Explanation of Solution

Given information:

A store that specializes in selling nuts has available $72pounds\left(Ib\right)$ of cashews and $120Ib$ of peanuts. These are to be mixed in $12-ounce\left(oz\right)$ packages as follows: a lower-priced package containing $8$ $oz$ of peanuts and $4$ $oz$ of cashews and a quality package containing $6$ $oz$ of peanuts and $6$ $oz$ of cashews.

Use $x$ to donate the number of lower-priced packages and use $y$ to denote the number of quality packages. Write a system of linear inequalities that described the possible number of each kind of package.

Calculation:

Consider number of lower-priced packages be $x$ , number of higher-priced packages $y$ .

The store contains total number of $72pounds\left(Ib\right)$ of cashews and $120Ib$ of peanuts.

The lower priced package has a total weight of $12ounce\left(oz\right)=0.75Ib$ and has $0.5pounds$ of peanuts and $0.25pounds$ of cashews, and the quality package has a total weight of $12ounce\left(oz\right)=0.75Ib$ and has $0.375pounds$ of peanuts and $0.375pounds$ of cashews.

Now modelled these conditions into inequalities as follows,

Amount of peanuts $=0.75x+0.375y\le 120$

Amount of cashews $=0.5x+0.375y\le 72$

Hence the inequalities are $\boxed{=0.75x+0.375y\le 120}$ , $\boxed{=0.5x+0.375y\le 72}$

b.

To determine

Graph the system and label the corner point.

Answer to Problem 104RE

  

Explanation of Solution

Given information:

A store that specializes in selling nuts has available $72pounds\left(Ib\right)$ of cashews and $120Ib$ of peanuts. These are to be mixed in $12-ounce\left(oz\right)$ packages as follows: a lower-priced package containing $8$ $oz$ of peanuts and $4$ $oz$ of cashews and a quality package containing $6$ $oz$ of peanuts and $6$ $oz$ of cashews.

Graph the system and label the corner point.

Calculation:

The system of inequalities be graphed by using graphing utility in rectangular cartisian coordinate system.

  

Hence, the result is shown in graph.