Question 1164719
To solve this, let's define the quantities of each model sold annually as variables:

*  = Number of units of **Model 1**
*  = Number of units of **Model 2**
*  = Number of units of **Model 3**

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### i. Joint Revenue Function

Revenue () is the total amount of money generated from sales. It is calculated by multiplying the wholesale price per unit by the quantity sold for each model.

### ii. Annual Cost Function

The total cost () consists of the **Fixed Costs** plus the **Variable Costs** (Material + Labor) for each unit produced.

**1. Calculate Variable Cost per unit ():**

* **Model 1:** 
* **Model 2:** 
* **Model 3:** 

**2. Formulate the function:**
Given the annual fixed costs are **$25,000,000**:


### iii. Profit Function

Profit ( or ) is the difference between the Total Revenue and the Total Cost.


Substitute the functions from the previous steps:


**Simplify the expression:**


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### Summary of Contribution Margins

This profit function reveals the **contribution margin** per unit for each model (the amount each sale contributes toward covering the $25M fixed costs):

| Model | Contribution Margin per Unit |
| --- | --- |
| **Model 1** | $225 |
| **Model 2** | $450 |
| **Model 3** | $525 |

Would you like me to calculate how many units of a specific model would need to be sold to reach the **break-even point**?