Write an objective function for the given situation. A tourist agency sells travel packages for a football game that include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. Each package with a non-stop flight sells for \( \$ 1200 \), and each package with a two-stop flight sells for \( \$ 900 \). The company wants to maximize their profit for the travel packages. All answer choices use \( x= \) non-stop packages, \( y= \) two-stop packages. \( P=2100 y \) \( P=900 x+1200 y \) \( P=2100 x \) \( P=1200 x+900 y \)

To formulate the objective function for the tourist agency's situation, we need to consider the profit generated from selling the travel packages. 1. **Identify the variables:** - Let \( x \) be the number of non-stop packages sold. - Let \( y \) be the number of two-stop packages sold. 2. **Determine the profit from each type of package:** - Each non-stop package sells for \( \$1200 \). - Each two-stop package sells for \( \$900 \). 3. **Formulate the total profit \( P \):** - The profit from non-stop packages is \( 1200x \). - The profit from two-stop packages is \( 900y \). 4. **Combine the profits to create the objective function:** \[ P = 1200x + 900y \] Thus, the correct objective function that the company wants to maximize is: \[ P = 1200x + 900y \] This corresponds to the answer choice \( P=1200 x+900 y \).