Question

An advertising agency offers two packages for small businesses who need advertising services. A basic package includes only design services. A premium package includes design and promotion. The agency's goal is to sell at least 60 packages in total.

The basic advertising package has a value of $1,000 and the premium package has a value of $2,500. The goal of the agency is to sell more than $60,000 worth of small-business advertising packages.
1. Write a system of inequalities to represent the constraints. Specify what each variable represents.
2. Use technology to graph the inequalities and sketch the solution regions. Include labels and scales for the axes.

Answer 1

The system of inequalities consists of two inequalities representing the total number of packages sold and the total value of the sold packages. Graphing the inequalities helps visualize the feasible solutions.

Step-by-step explanation:

1. Let's use the variables B and P to represent the number of basic packages and premium packages sold, respectively.

Based on the information given, we can write the following system of inequalities:

• B + P > 60 (At least 60 packages need to be sold in total)
• 1000B + 2500P > 60000 (The total value of the packages sold needs to be more than $60,000)

2. To graph these inequalities, plot the two lines B + P = 60 and 1000B + 2500P = 60000. Then shade the region above both lines to represent the feasible solutions.