Chapter 11, Problem 58RE

(a)

To determine

To find: The system of linear inequalities that describes the possible number of each kind of package.

Answer to Problem 58RE

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

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

Explanation of Solution

Given information:

The given, selling nuts available is $72pounds$ of cashews and $120pounds$ of peanuts.

Total both package weight is $12-ounce$ .

Lower-price of peanuts $8-ounce$ and the cashews $4-ounce$ .

Quality package contains $6-ounce$ of peanuts, and $6-ounce$ of cashews.

Calculation:

The lower price package has total weight $12-ounce=0.75pounds$ , and peanut $=0.5pounds$ , and cashews $=0.25pounds$ .

The quality price package has total weight $12-ounce=0.75pounds$ , and peanut $=0.375pounds$ , and cashews $=0.375pounds$ .

Therefore, the condition is,

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

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

(b)

To determine

To graph: the linear equation and graph.

Explanation of Solution

Given:

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

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

Graph:

The graph of the equation is shown in figure-(1)

  

Figure $\left(1\right)$

The linear equation is graph in Figure $\left(1\right)$ .