Francine sells advertising time packages for a local television station. She is able to make up to 15 sales calls per week offering potentila advertisers either a prime time package for`$12,000` or a non prime time package for `$8,000.` Her weekly sales goal is to sell more than `$20,000` worth of advertising. Which of the following systems of inequalities represents this situation in terms of p, the number of prime time packages Francine sells in a week, n, the number of non prime time packages, and u, the number of unsuccessful sales calls for whihic she sells neither offering ?

Options

A. `p+n + u le 15`
`12, 000 p + 8, 000 n gt 20, 000`
B. `p +n + u ge 15`
`12, 000 p + 8,000 n gt 20, 00`
C. `p +n + u le 15`
`12, 000 p+ 8,000 (n+u) gt 20,000`
D. `p + n + u le 15`
`12, 000 p + 8, 000n lt 20, 000`

Explanation

To solve the problem, we need to set up a system of inequalities based on the information provided about Francine's sales calls and her sales goals.

1. **Identify Variables:**
- Let \( p \) = number of prime time packages sold.
- Let \( n \) = number of non-prime time packages sold.
- Let \( u \) = number of unsuccessful sales calls.

2. **Set Up the Inequalities:**
- Francine can make a maximum of 15 sales calls per week. Therefore, the total number of calls (successful and unsuccessful) must be less than or equal to 15:
\[ p + n + u \leq 15 \]

- Francine's weekly sales goal is to sell more than $20,000 worth of advertising. The revenue from selling \( p \) prime time packages at $12,000 each and \( n \) non-prime time packages at $8,000 each must be greater than $20,000:
\[ 12,000p + 8,000n > 20,000 \]

3. **Final System of Inequalities:**
The system of inequalities that represents Francine's situation is:
\[ \begin{align*} 1. & \quad p + n + u \leq 15 \\ 2. & \quad 12,000p + 8,000n > 20,000 \end{align*} \]