Question

A home security company plans to open a calling center to respond to customer calls and

emails. They plan to buy a large building with one large room to place cubicles where
operators will work. There are two options for cubicles: small cubicles for one operator that
is 49 square feet and larger cubicles for two operators that is 80 square feet. The company
knows it wants a minimum of 12 cubicles, but because of the expense of additional
employees, they want a maximum of 20 operators.



Write a system of inequalities to model the calling center that would help the company
determine the number of cubicles to build and the number of operators to be employed.
Define any variables used.

Answer 1

`x+y\geqslant 12`

`x+2y\leqslant 20`

Explanation:

Inequalities

The home security company will choose between two options for cubicles: the small cubicle for only one operator and the large cubicle to hold 2 operators. Let x be the number of small cubicles and y the number of large cubicles. Since each small cubicle has 49 square feet, the total area occupied by them will be 49x. Each large cubicle occupies 80 square feet, so the y cubicles use 80y square feet. The total area used by them is

Area=49x+80y

Assuming there is no operator without cubicle and all cubicles are fully occupied, the number of operators will be

Operators=1x+2y=x+2y

The number of cubicles is

# cubicles=x+y

The conditions of the problem state that

`x+y\geqslant 12`

`x+2y\leqslant 20`