4.05 Systems of linear inequalities
Interactive practice questions
An airline is checking passengers into two flights, A and B, simultaneously. Due to passenger numbers, there must be at least $10$10 staff at check-in for flight A and at least $7$7 staff at check-in for flight B. Since there must be staff on hand for other services, the airline can only allocate at most $23$23 staff for check-in of both flights.
Let $x$x and $y$y represent the number of staff attending check-in of flights A and B respectively.
Fill in the gaps to complete the system of inequalities.
$x$x $\ge$≥ $\editable{}$
$y$y $\ge$≥ $\editable{}$
$x+y$x+y $\le$≤ $\editable{}$
Graph the system of inequalities.
If $14$14 staff are allocated to checking in passengers of flight A, what is the maximum number of staff that can be allocated to checking in passengers of flight B?
Throughout university, Luigi works as a mentor, getting paid $\$10$$10 per hour, and as a barista getting paid $\$13$$13 per hour. The number of hours he works in each job can vary from week to week, and he needs to be able to at least cover his weekly expenses of $\$260$$260.
Roald has $24$24 inches of leftover wood that he is trying to make a rectangular photo frame out of.