Mathematics for Business Decisions, Part II

Project 1. Marketing a Product

Final Report

Prepared for:

Kerima Ratnayaka

Math 115b, Section __18___

University of Arizona

Submitted by:

Team _____

on

date

Table of Contents

We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course.

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Name (printed) Signature

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I.  Background

II.  Objectives

III.  Assumptions

IV.  Given Data

Potential national market:
Test Markets
Market Number / Market Size / Price / Projected Yearly Sales (number of units)
1
2
3
4
5
6
7
8
Fixed Cost For The Year:
Variable Costs
Quantity / Cost per unit
First
Next
Further:

V.  Demand, Revenue, Cost and Profit Functions

A.  Definitions of , , , and

B.  Graph of Projected Yearly Sales in National Market and Trend Line

(with source data)

C.  Demand Function (formula and graph)

D.  Revenue and Cost Functions (formulas and graph)

E.  Profit Function (formula and graph)

F.  Discussion

VI.  Marginal Revenue, Cost, and Profit Functions

A.  Definitions of , , and

B.  Formula for

C.  Marginal Revenue and Marginal Cost Functions (formulas and graph)

D.  Marginal Profit Function (formula and graph)

E.  Discussion

VII.  Recommendations

A.  Optimal Price, Quantity, and Maximum Profit

  1. Function

  1. Results (display computation cells)

B.  Sensitivity of Profit to Changes in Optimal Price (display computation cells)

C.  Consumer Surplus When Profit is Maximized

1.  Definition of Consumer Surplus

2.  Formula and Computation

D.  Profit at Given Price (display computation cells)

E.  Change in Demand

1.  New Demand Function

2.  Change in Profit and Optimal Price (display computation cells)

F.  Training and Streamlining

1.  New Cost Function

2.  Change in Profit (display computation cells)

VIII.  Further Analysis

IX.  Conclusion

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