Chapter 5.7, Problem 29E

(a)

To determine

To graph: the system of linear inequalities that represent the situation.

Answer to Problem 29E

The graph of system of linear inequalities is drawn.

Explanation of Solution

Given:

Blueberries cost $4$ dollars per pound and strawberries cost $3$ dollars per pound.

It needs at least $3$ pounds of fruits and it can spend maximum of $21$ dollars on fruits.

Concept used:

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but the area of the coordinate plane that satisfy the inequality. the boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ The common area is the solution of inequality.

Calculation:

Blueberries cost $4$ dollars per pound and strawberries cost $3$ dollars per pound.

It needs at least $3$ pounds of fruits and it can spend maximum of $21$ dollars on fruits.

Write the system of linear inequalities that models the given problem.

Check whether it can buy $4$ pounds of blueberries and $1$ pound of strawberry.

Let $x$ be the pound of blueberries and $y$ be the pounds of strawberries. Then the system of inequalities that models the given problem is:

  $\begin{array}{l}x+y\ge 3.\\ 4x+3y\le 21.\end{array}$

the system of linear inequalities is:

  $x+y\ge 3\text{ and }4x+3y\le 21$ .

Graph of the inequalities $y\ge -x+3\text{ and }y\le -\frac{4}{3}x+7$ :

Hence, the graph of system of linear inequalities is drawn.

(b)

To determine

To find: the solution of the system.

Answer to Problem 29E

It means that it can buy $2$ blueberries and $4$ straw berries.

Explanation of Solution

Given:

Blueberries cost $4$ dollars per pound and strawberries cost $3$ dollars per pound.

It needs at least $3$ pounds of fruits and it can spend maximum of $21$ dollars on fruits.

Concept used:

The difference is that a solution to the inequality is not the drawn line but area of the coordinate plane that satisfy the inequality.

The common area is the solution of inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

Blueberries cost $4$ dollars per pound and strawberries cost $3$ dollars per pound.

It needs at least $3$ pounds of fruits and it can spend maximum of $21$ dollars on fruits.

Write the system of linear inequalities that models the given problem.

Check whether it can buy $4$ pounds of blueberries and $1$ pound of strawberry.

Let $x$ be the pound of blueberries and $y$ be the pounds of strawberries. Then the system of inequalities

The intersection of blue and red colours represents the solution set of given problem.

For example, the ordered pair $\left(x,y\right)=\left(2,4\right)$ is in the solution set.

Hence, it means that it can buy $2$ blueberries and $4$ straw berries.