Question

I need to know how to solve this question and how to do these things on my rubric Represent the other quantities in terms of XAnswer the question in complete sentences

Answer 1

The number of units given that the company has an average cost of $100 per unit is 460 units

SOLUTION

Problem Statement

The question tells us a company's fixed cost is $11,500 while it costs $75 per unit for each unit they produce. We are asked to find the number of units produced by the company that would result in an average cost per unit of $100.

Method

- The fixed cost of a company is the cost of all the operations whose cost never changes.

- The production cost of $75 per unit represents the cost of producing one unit of their product.

- Thus, we can ascertain the total production cost of the company by adding the Fixed cost to the Production cost. That is:

`\text{Total Cost }=\text{ Fixed cost }+\text{ Production cost}`

- The average cost of a company is simply the average cost of running the company per every unit of production. Simply put, it is the ratio of the total cost and the number of units produced.

Thus, we can say that:

`\text{Average cost }=\frac{\text{Total Cost}}{\text{Number of units produced}}`

- It is with the above formula we shall solve the question.

Implementation

- To apply the Average cost formula, we need to first find the Total cost. Total cost is made up of Fixed cost and Production cost.

`\begin{gathered} \text{Fixed cost}=11,500 \\ \text{Production cost for 1 unit}=75\text{ for 1 unit.} \\ \text{ Production cost for n units }=75* n=75n \\ \\ \therefore\text{Total cost }=Fixed\text{ cost + Production cost} \\ \\ Total\text{ cost}=11,500+75n \end{gathered}`

- Now that we have the expression for Total cost, we can proceed to use the formula for average cost above

`\begin{gathered} \text{Average cost}=100 \\ \text{Total cost}=11,500+75n \\ \text{Number of units produced}=n \\ \\ \therefore\text{Average cost}=\frac{\text{Total Cost}}{\text{Number of units produced}} \\ \\ 100=(11,500+75n)/(n) \\ \text{Cross-multiply} \\ 100n=11,500+75n \\ \text{Subtract 75n from both sides} \\ 100n-75n=11,500 \\ 25n=11500 \\ \text{Divide both sides by 25} \\ (25n)/(25)=(11500)/(25) \\ \\ \therefore n=460\text{units} \end{gathered}`

Summary of Solution

To solve this question, we followed these steps:

1. We found the expression for the total cost of the company.

`\begin{gathered} \text{Total cost}=\text{ Fixed cost }+\text{ Production cost} \\ \text{Total Cost }=11,500+75n \\ \\ \text{where, } \\ n=\text{The number of units produced} \end{gathered}`

2. We applied the formula given below to find the number of units produced (n).

`\text{Average cost}=\frac{\text{Total cost}}{\text{Number of units produced}}`

Final Answer

The number of units given that the company has an average cost of $100 per unit is 460 units