Example 1
Completion requirements
| Example 1 |
Steve works in a restaurant some evenings and earns \(\$12 \rm{/h}\). He also moves furniture on the weekends for \(\$14 \rm{/h}\). Steve is planning to buy a new laptop for \(\$1\thinspace 350\). Graph all the possible combinations of hours worked that will allow Steve to buy the new laptop.
Let \(R\) be the number of hours Steve works at the restaurant and let \(F\) be the number of hours he moves furniture. His earnings from the restaurant are \(12R\) and his earnings from moving furniture are \(14F\).
\(12R + 14F \ge 1 \thinspace 350\)
Graph the inequality by hand or using technology. A negative number of hours worked is not possible, so only positive \(R\) and \(F\) values are included.
The graph shows all the possible combinations of hours worked that will allow Steve to buy the new laptop. Note that the shaded region (solution region) of the graph extends indefinitely up and to the right.
\(12R + 14F \ge 1 \thinspace 350\)
Graph the inequality by hand or using technology. A negative number of hours worked is not possible, so only positive \(R\) and \(F\) values are included.
The graph shows all the possible combinations of hours worked that will allow Steve to buy the new laptop. Note that the shaded region (solution region) of the graph extends indefinitely up and to the right.
| For further information about linear inequalities in two variables, see pp. 464 – 471 of Pre-Calculus 11. |