Question

SA school has 900 concert tickets for sale. Some of them are for reserved seats (x) and the

rest are for general admission (y). No more than 600 reserved seat tickets can be sold. They
know they will sell at least 200 general admission tickets. Write a system of inequalities that
shows how many of each type of ticket can be sold and then graph the feasible region.

Answer 1

• x ≤ 600
• y ≥ 200
• x +y ≤ 900
• see the attachment for a graph

Explanation:

Given 900 tickets for sale and restrictions on the numbers of reserved and general admission seats, you want a system of inequalities that models the possible sales. You also want a graph of the feasible region.

The variables are defined as ...

• x = number of reserved seat tickets
• y = number of general admission tickets

Inequalities

The limits give rise to these inequalities:

x ≤ 600 . . . . . no more than 600 reserved seats can be sold

y ≥ 200 . . . . . at least 200 general admission tickets will be sold

x + y ≤ 900 . . . . at most, 900 tickets can be sold

Graph

These inequalities can be graphed simply by giving them as input to a graphing calculator. The result is attached. The feasible region is that area of the graph where the three solution spaces overlap. Here, it is outlined in black.