SOLUTION: A Manufacturer of microcomputers produces three different models as shown in Table 2. The following summarizes wholesale prices, material cost per unit, and labor cost per unit.

Question 1164719: A Manufacturer of microcomputers produces three different models as shown in Table 2.
The following summarizes wholesale prices, material cost per unit, and labor cost per unit.
Annual fixed cost are $25 million.

Model 1 Model 2 Model 3

Wholesale price/unit 500 1000 $1500
Material Cost / unit 175 400 750
Labor cost / unit 100 150 225

i. Determine a joint revenue function for sales of the three different microcomputer models
ii. Determine the annual costs function for the manufacturing the three models.
iii. Determine the profit function for sales of the three models?

Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(2189)   (Show Source): You can put this solution on YOUR website!
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**
---
### 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:**

---
### 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**?
Answer by ikleyn(53618)   (Show Source): You can put this solution on YOUR website!
.
A Manufacturer of microcomputers produces three different models as shown in Table 2.
The following summarizes wholesale prices, material cost per unit, and labor cost per unit.
Annual fixed cost are $25 million.

Model 1 Model 2 Model 3 Wholesale price/unit $500 $1000 $1500 Material Cost / unit $175 $400 $750 Labor cost / unit $100 $150 $225

i. Determine a joint revenue function for sales of the three different microcomputer models
ii. Determine the annual costs function for the manufacturing the three models.
iii. Determine the profit function for sales of the three models?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The content of the post by @CPhill is outright nonsense of the undebugged computer code.
It is irrelevant to the problem and to its adequate solution.
So, simply ignore the post by @CPhill for the safety of your mind.

See my correct solution below.

(i) The joint revenue function is the function of three arguments (n1,n2,n3), where n1 is the number of units of Model 1, n2 is the number of units of Model 2, and n3 is the number of units of Model 3 produced per year. The joint revenue function is R(n1,n2,n3) = 500*n1 + 1000*n2 + 1500*n3. ANSWER to (i) Part (i) is solved. (ii) The annual cost function is the function of three arguments (n1,n2,n3), where n1 is the number of units of Model 1, n2 is the number of units of Model 2, and n3 is the number of units of Model 3 produced per year. The annual cost function is C(n1,n2,n3) = 25000000 + (175+100)*n1 + (400+150)*n2 + (750+225)*n3. = 25000000 + 275*n1 + 550*n2 + 975*n3. ANSWER to (ii) Part (ii) is solved. (iii) The profit function is the function of three arguments (n1,n2,n3), where n1 is the number of units of Model 1, n2 is the number of units of Model 2, and n3 is the number of units of Model 3 produced per year. The profit function is P(n1,n2,n3) = R(n1,n2,n3) - C(n1,n2,n3) = (500-275)*n1 + (1000-550)*n2 + (1500-975)*n3 - 25000000. = 225*n1 + 450*n2 + 525*n3 - 25000000. ANSWER to (iii) Part (iii) is solved.

Solved completely.

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                Regarding the post by @CPhill . . .

Keep in mind that @CPhill is a pseudonym for some artificial intelligence computer code
(!! some just very outdated version !! ).

The artificial intelligence in solving Math problems is in the experimental stage of development
and it is far from to be a well-tuned.
It can make mistakes and produce nonsense.

                It has no feeling of shame - it is shameless.

This time, again, it made an error.

The @CPhill' solutions are copy-paste AI solutions (of its just old outdated version), but there is one essential difference.

Every time, normal AI makes a note at the end of its solutions that Google AI is experimental
and can make errors/mistakes.

All @CPhill' solutions are copy-paste of AI solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So, he NEVER SAYS TRUTH.

Every time, @CPhill embarrassed to tell the truth.
But I am not embarrassing to tell the truth, as it is my duty at this forum.

And the last my comment.

When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
until the specialists and experts will check and confirm their correctness.

Without it, their reliability is ZERO and their creadability is ZERO, too.

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