Chapter 5.7, Problem 30E

(a)

To determine

The graph of the system of linear inequalities that represents the situation.

Answer to Problem 30E

  $10x+15y\ge 120$

Explanation of Solution

Given information:

You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour you also teach to earn at least $120 per week. but you do not want to work more than 20 hours per week.

Formula used:

Substitution method is used.

Calculation:

Let:

  $\begin{array}{l}x\to \text{number of hours worked in grocery store}\\ y\to \text{number of hours teaching music lessons}\end{array}$

Set up the inequalities:

Working time no more than 20 hours

  $x+y\le 20$

Earnings of at least $120

  $10x+15y\ge 120$

Required to work at least 8 hours at the grocery store

  $x\ge 8$

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

Graph the equations:

The solution is the intersection:

  

Conclusion:

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

(b)

To determine

the solution of the system.

Answer to Problem 30E

Hours working at the grocery store & 4 hours teaching music lessons

Explanation of Solution

Given information:

You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour you also teach to earn at least $120 per week. but you do not want to work more than 20 hours per week.

Formula used:

Substitution method is used

Calculation:

  $\left(14,4\right)\to 14$ Hours working at the grocery store & 4 hours teaching music lessons

Conclusion:

Hours working at the grocery store & 4 hours teaching music lessons

(c)

To determine

To work 8 hours in grocery store to teach 1 hour music lesson.

Answer to Problem 30E

The point (8, 1) is NOT on the shaded region.

Explanation of Solution

Given information:

You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour you also teach to earn at least $120 per week. but you do not want to work more than 20 hours per week.

Formula used:

Substitution method is used

Calculation:

No, because point (8, 1) is NOT on the shaded region.

Conclusion:

No, because point (8, 1) is NOT on the shaded region.