# Cost-Volume-Profit Analysis Investigation Project – Chapter 8

Ana Duff, adapted from work by J. Olivier and D. Lippman

## Modeling data for Cost-Volume-Profit Analysis

### Getting the data

2. #### Get the data:

1. Download the Excel file CVP Analysis Data.
2. Save the document.

### Cost model

1. #### Select the data in cost-production worksheet and copy into Cost folder

• Make note that the data variables created by Desmos are $x_1$ and $y_1$. You can change these but will have to make the corresponding changes to formulas used below as well.
1. #### Analyze the data trend and decide on an appropriate function type to model the cost data

• Cost data appears to follow a linear trend
• Should try $C(x)=mx+b$
1. #### Create an appropriate cost function model using the Desmos regression tool

• In Cost folder, add y1~mx1+b to a new line in the folder
1. #### Write the cost function model and plot it:

• In Cost folder, add the appropriate formula for , with appropriate domain restrictions;
• Hide the regression model and the data.

1. #### Record in your CVP Analysis Summary document the cost function model and its domain.

Price-demand model

1. #### Adjust scaling of the axes for a better view

• Click on Graph Settings tool and adjust the horizontal and vertical view window.
1. #### Analyze the data trend and decide on an appropriate function type to model the cost data

• Price-demand data appears to follow a quadratic trend
• Should try $p(x)=ax^2+bx+c$
1. #### Create an appropriate price-demand function model using the Desmos regression tool

• In price-demand folder, add y2~ax2^2+bx2+c
1. #### Write the cost function model and plot it

• In Price-demand folder, add the appropriate formula for , with appropriate domain restrictions;
• Hide the regression model and the data.

### Revenue model

1. #### Adjust scaling of the axes for a better view

• Zoom out until the whole graph is visible, then click on Graph Settings tool and adjust the horizontal and vertical view window.

2. #### Enter into your CVP Analysis Summary document the following:

1. the revenue function model
2. the maximum revenue amount and when it occurs (demand and price).

### Profit model

2. #### Enter into your CVP Analysis Summary document the following:

1. the profit function model
2. the maximum profit amount and when it occurs (demand and price).

### Cost-volume-profit analysis chart

1. #### Adjust scaling of the axes for a better view

• Zoom out until all three graphs are fully visible, then click on Graph Settings tool and adjust the horizontal and vertical view window.

1. #### Add points of interest to the graph: fixed cost, maximum revenue, maximum cost, maximum profit and break-even points

• Click on the graph around each point of interest and note the value of the point as identified by Desmos;
• Plot and label each point on the graph.

1. #### Mark regions of profit and loss

• Plot area where revenue is higher than cost: ;
• Plot area where cost is higher than revenue: .

1. #### Finalize the CVP Analysis Graph

• Minimize CVP folder;
• Add graph arrows and axes titles using Graph Settings tool.

1. #### Complete your CVP Analysis Summary document by adding the following:

1. the break-even demand, price and revenue
2. the link to the graph through Share Your Graph – Copy Link tool and insert it into the Word document;
3. the image of the graph by first downloading it using Share Your Graph – Export Image tool, then copying into the submission document.

THE END

Attribution: Created by Ana Duff (Ontario Tech University), published under Creative Commons Attribution-NonCommercial-ShareAlike licence (CC-BY-NC-SA)

Any modifications to this case study may affect its solvability and caution is advised.