Chapter 5.7, Problem 29E

(a)

To determine

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

Answer to Problem 29E

  $y=-x+3\left(\text{shade upper half}\right)$

  $y=-\frac{4}{3}x+7\left(\text{shade lower half}\right)$

Explanation of Solution

Given information:

The amount spends on $21 on fruit. The blue berries cost $3 per pound. It is required atleast 3 pounds to make the fruit muffins.

Let:

  $\begin{array}{l}x\to \text{amount of blueberries in pounds}\\ y\to \text{amount of strawberries in pounds}\end{array}$

Set up the inequalities:

At least a total 3 pounds

  $x+y\ge 3$

At most $23 on cost

  $4x+3y\le 21$

Restrict the graph to positive x & y values since negative values do not make sense in this real-life context.

Graph the equations:

  $\begin{array}{l}x+y=3\\ y=-x+3\left(\text{shade upper half}\right)\&\\ 4x+3y=21\\ y=-\frac{4}{3}x+7\left(\text{shade lower half}\right)\end{array}$

The solution is the dark shaded area:

  

Conclusion:

The graph to positive x & y values since negative values do not make sense in this real-life context.

(b)

To determine

To find: The solution of the system.

Answer to Problem 29E

3 Pounds of blueberries & 1 pound of strawberries

Explanation of Solution

From the graph the point (3, 1) lies under the solution part so it is one solution of the system. $\left(3,1\right)\to 3$ Pounds of blueberries & 1 pound of strawberries

(c)

To determine

To use: The graph to check if 4 pounds of mulberries and 1 pound of strawberries fits in the solution.

Answer to Problem 29E

Yes, (4, 1) is on the shaded region.

Explanation of Solution

One can buy 4 pounds of berry and 1 pound of berries as the point (4, 1) is within the shaded region.