Chapter 7.5, Problem 70E

(A)

To determine

To find:

The solution set of the system of inequalities for the different amounts of food $X$ and food $Y$

Answer to Problem 70E

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\\ x\ge 0\\ y\ge 0\end{array}$

Explanation of Solution

Given:

The equation

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for <or> and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

Let $x$ = amount of food $X$

  $y$ = amount of food $Y$

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Both foods must be equal or greatorthan $0$

  $\begin{array}{l}x\ge 0\\ y\ge 0\end{array}$

The system of inequality

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\\ x\ge 0\\ y\ge 0\end{array}$

(B)

To determine

To find:

The solution set of the system of inequalities for the different amounts of food $X$ and food $Y$

Answer to Problem 70E

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Explanation of Solution

Given:

The equation

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

Let $x$ = amount of food $X$

  $y$ = amount of food $Y$

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\\ x\ge 0\\ y\ge 0\end{array}$

Draw the table

$x-axis$	$5$	$13.33$	$10$	$0$
$y-axis$	$7.5$	$3.33$	$0$	$15$

Draw the graph

  

(C)

To determine

To find:

The solution set of the system of inequalities for the different amounts of food $X$ and food $Y$

Answer to Problem 70E

  $x=20,y=20$ , $x=15,y=30$

Explanation of Solution

Given:

The equation

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

Let $x$ = amount of food $X$

  $y$ = amount of food $Y$

  $\begin{array}{l}20x+10y\ge 300\\ 15x+10y\ge 150\\ 10x+20y\ge 200\end{array}$

Take any two points that is the region bounded from part (b)

  $x=20,y=20$

In take of $20$ ounces of food $X$ and $20$ ounces of food $Y$

  $x=15,y=30$

In take of $15$ ounces of food $X$ and $30$ ounces of food $Y$