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Answer :
To solve this problem, we need to set up a system of inequalities based on the conditions Joyce has for placing advertisements in magazines V and E. Let's break down the conditions:
1. Reach Condition:
- Each ad in magazine V reaches 1.5 million people.
- Each ad in magazine E reaches 1.2 million people.
- Joyce wants to reach at least 7 million readers in total.
Therefore, the inequality for reaching at least 7 million people is:
[tex]\[
1.5x + 1.2y \geq 7
\][/tex]
2. Minimum Ads Condition:
- Joyce wants to place at least 2 ads in magazine V. This gives us:
[tex]\[
x \geq 2
\][/tex]
- Similarly, Joyce wants to place at least 2 ads in magazine E. This results in:
[tex]\[
y \geq 2
\][/tex]
Now, let's summarize the system of inequalities that describes these conditions:
- Reach Condition: [tex]\(1.5x + 1.2y \geq 7\)[/tex]
- Ads in Magazine V: [tex]\(x \geq 2\)[/tex]
- Ads in Magazine E: [tex]\(y \geq 2\)[/tex]
These inequalities can be used to graph the feasible region. To graph this:
- Draw the line for [tex]\(1.5x + 1.2y = 7\)[/tex].
- Shade the region that satisfies [tex]\(1.5x + 1.2y \geq 7\)[/tex], which is above the line.
- Also draw the vertical line for [tex]\(x = 2\)[/tex] and shade the region where [tex]\(x \geq 2\)[/tex].
- Draw the horizontal line for [tex]\(y = 2\)[/tex] and shade the region where [tex]\(y \geq 2\)[/tex].
The intersection of these shaded regions represents the feasible region where all conditions are met. The points in this region will tell Joyce how many ads she should place in each magazine to meet her goals.
1. Reach Condition:
- Each ad in magazine V reaches 1.5 million people.
- Each ad in magazine E reaches 1.2 million people.
- Joyce wants to reach at least 7 million readers in total.
Therefore, the inequality for reaching at least 7 million people is:
[tex]\[
1.5x + 1.2y \geq 7
\][/tex]
2. Minimum Ads Condition:
- Joyce wants to place at least 2 ads in magazine V. This gives us:
[tex]\[
x \geq 2
\][/tex]
- Similarly, Joyce wants to place at least 2 ads in magazine E. This results in:
[tex]\[
y \geq 2
\][/tex]
Now, let's summarize the system of inequalities that describes these conditions:
- Reach Condition: [tex]\(1.5x + 1.2y \geq 7\)[/tex]
- Ads in Magazine V: [tex]\(x \geq 2\)[/tex]
- Ads in Magazine E: [tex]\(y \geq 2\)[/tex]
These inequalities can be used to graph the feasible region. To graph this:
- Draw the line for [tex]\(1.5x + 1.2y = 7\)[/tex].
- Shade the region that satisfies [tex]\(1.5x + 1.2y \geq 7\)[/tex], which is above the line.
- Also draw the vertical line for [tex]\(x = 2\)[/tex] and shade the region where [tex]\(x \geq 2\)[/tex].
- Draw the horizontal line for [tex]\(y = 2\)[/tex] and shade the region where [tex]\(y \geq 2\)[/tex].
The intersection of these shaded regions represents the feasible region where all conditions are met. The points in this region will tell Joyce how many ads she should place in each magazine to meet her goals.
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Rewritten by : Barada
