Chapter 5.7, Problem 31E

(a)

To determine

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

Answer to Problem 31E

The system of linear inequality is:

  $x\le 15,y\le 10\text{ and }x+y\le 20.$

Explanation of Solution

Given:

Gaming laws allow to catch no more than $15$ surfperch per day, no more than $10$ rockfish per day and no more than $20$ total bottom fish per day.

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:

Gaming laws allow to catch no more than $15$ surfperch per day, no more than $10$ rockfish per day and no more than $20$ total bottom fish per day.

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

Determine whether it can $11$ surfperch and $9$ rockfish per day.

Let $x$ be the number of surfperch and $y$ be the number of rockfish.

Then the system of inequalities that models the given problem is:

  $\begin{array}{l}x\le 15.\\ y\le 10.\\ x+y\le 20.\end{array}$

The graph of the inequality’s equation $x\le 15,y\le 10\text{ and }x+y\le 20$ is:

hence, the system of linear inequality is:

  $x\le 15,y\le 10\text{ and }x+y\le 20.$

(b)

To determine

To find: whether the person can catch $11$ surfperch, $9$ rockfish in $1$ day.

Answer to Problem 31E

The answer is yes.

Explanation of Solution

Given:

Gaming laws allow to catch no more than $15$ surfperch per day, no more than $10$ rockfish per day and no more than $20$ total bottom fish per day.

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:

The intersection of pink, blue and green colours represent the solution set of given problem.

The ordered pair $\left(x,y\right)=\left(11,9\right)$ is in the solution set. It means $11$ surfperch and $9$ rockfish can be caught per day.

Hence, the answer is yes.