# Case Study – Chapter 7 (Compound Inequalities)

Morden Shapiro

## Lease Contingency Payments

### Background

John has leased retail space in a regional shopping mall. His rent arrangement includes a fixed monthly amount that reflects current square footage charges in the local area. He is content with that fixed amount and has no issue with it.

However, the lease arrangement also includes a contingency component that is tied to his total annual sales in three product areas. This component is:

Product A – 5% of annual sales in excess of \$200,000 (the “threshold”).

Product B – 2% of annual sales in excess of \$350,000 (the “threshold”).

Product C – 15% of annual sales in excess of \$80,000 (the “threshold”).

John has engaged a marketing consultant to perform research to establish the likely sales amounts that can be achieved for each of the three products. The marketing consultant has told him that the resulting sales figures will be within a range of error of 2%.

The marketing consultant has determined that likely sales in these product areas will be:

Product A \$265,000.

Product B \$375,000.

Product C \$78,000.

John will use this information to budget his annual rent cost including the contingency component.

### Assignment

In mathematical terms express John’s ranges of likely contingency payments based on the information provided above.

### Challenge

The marketing consultant has told John that for an additional fee she could extend her research model so that the results of the research would be given with a range of error of 1.5%. Using your response to Assignment, answer the following question:

Which mathematical strategy would you use to determine the maximum additional fee for the marketing consultant that would be economically worthwhile for John to incur in order to have a reduced range of error? Explain your answer.

Attribution: Case study by Morden Shapiro (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.