Answer to Question #329271 in Linear Algebra for Busi

Question

A local high school needs to hire several cafeteria workers and bus drivers. Cafeteria workers earn R13 800

per month and bus drivers earn R17 250 per month. The school board gave the school permission to spend

no more than R345 000 on the salaries per month, but must hire more than 15 people.

Let B represent the number of bus drivers hired.

Let C represent the number of cafeteria workers hired.

For every bus driver hired there must be at least two cafeteria workers hired. The number of cafeteria

workers must at most be three more than twice the number of bus drivers.

Write a system of linear inequalities that the school could use to determine the number of cafeteria workers

and bus drivers they can hire

Answer 1

$17250b+13800c\le 345000\\ b+c\gt 15 \\ c\ge 2b \\ c\le 2b+3 \\$

One can check that the following pairs are solutions: b=5 and c=11; b=5 and c=12; b=5 and c=13; b=6 and c=12; b=6 and c=13; b=6 and c=14; b=6 and c=15; b=7 and c=14; b=7 and c=15; b=7 and c=16.