Systems of equations are used in many cost models in the real world.

Full Answer Section

      Solving this system using substitution or elimination methods will give you: * H = 75 hamburgers * S = 45 sodas

2. Rebalancing Consumption with Price Adjustments:

• Goal: Change price ratio to encourage more balanced consumption of hamburgers and sodas.
• Strategy: Increase soda price relative to hamburgers, making them closer in cost.
• New Prices: (Possible options)
  • Option 1: Hamburger = $1.75, Soda = $1.00
  • Option 2: Hamburger = $1.50, Soda = $0.90

These choices aim to make both options roughly equally appealing in terms of cost per unit (e.g., $1.75/burger vs. $1/soda in option 1).

• New Sales Calculation: With the new prices, you would need to recalculate the number of hamburgers and sodas sold using the same system of equations with updated price values.

3. Comparing Your Peer's Example:

Unfortunately, I don't have access to your peer's specific example for comparison. However, I can offer some general points for analysis:

• Similarities: Both scenarios likely involve using systems of equations with price and quantity variables to model a real-world cost scenario.
• Differences: The specifics of the scenario (industry, products, prices, goals) will differ. Your carnival example focuses on balancing consumption, while your peer's example might have a different objective, such as maximizing profit or meeting specific demand conditions.
• Relevance to Your Profession: Systems of equations are versatile tools applicable in various professions, including healthcare, finance, business, and engineering. They allow you to model and analyze complex relationships between variables and make informed decisions based on the results.

4. Changes to the Equations:

The proposed price adjustments are reasonable for their intended purpose. By making sodas relatively more expensive, the goal is to discourage their excessive consumption and create a more balanced purchasing preference towards hamburgers.

5. Citations and References:

• Chang, A. T., & Gerald, K. F. (2015). Applied mathematical modeling for business and management. John Wiley & Sons.
• Nagle, T. T., & Martin, S. E. (2018). Decisionmaking with marketing models. Pearson.
• Shahian, F., & Smith, G. (2021). Systems of equations: Algebra II: A complete introduction. Independently published.

This analysis provides a framework for understanding how systems of equations can be used to model and solve real-world cost scenarios. By adjusting prices and analyzing the resulting changes in consumption, you can optimize your business goals and achieve desired outcomes.  

Sample Solution

     

Carnival Scenario: Analyzing Cost Models with Systems of Equations

1. Carnival Profits and Equations:

• Given: Hamburger price = $1.75, Soda price = $0.75, Target revenue = $117.50, Total items sold = 120 (hamburgers+sodas).

• Problem: Find the number of hamburgers and sodas sold.

• Solution: This can be modeled using a system of two equations:

  • Equation 1: 1.75H + 0.75S = 117.50 (Revenue equation)
  • Equation 2: H + S = 120 (Total items equation)