Shipping Wars

 

Project Overview

 

Purpose

 

You will be relating and explaining the concepts from Module 7 to a transportation business.

 

Process

 

Toward the end of each lesson, under Project Connection, you may be prompted to complete a part of the Module 7 Project.

 

Make sure to save all work from each Project Connection in your course folder. You will submit your entire Module 7 Project to your teacher at the end of Module 7. Make sure to show all your work.

 

Presentation

 

The most important part of your project presentation is to clearly explain and support your reasoning with relevant visuals and calculations.

 

Carefully check the Module 7 Project Rubric to be sure you are clear about the expectations for the project.

 

You can choose any format you prefer for the final presentation of this project. Some options include a written document, a virtual or real poster, a website, a video, an oral report, or a slideshow presentation.

 

Project Introduction

 

Shipping is a challenging business for an entrepreneur to set up and build. Generally, a shipping company starts out with a few people and a few trucks in one location. The kinds of products you ship, their weight, the distances to ship, and your customer needs are all factors in the nature of your business. A key to growth is to reach out to new prospects and expand to multiple locations whenever you have the financial means.

 

You have decided to open and manage a shipping company. Like all new businesses, you will need to plan to help attract and keep customers as well as manage your finances.

 

Part 1

 

Read all of Part 1 before beginning.

1. Decide on the type of objects you will be shipping and the method of transportation. Research the capacity of the vehicle type you plan to use, and possibly your product, to determine the maximum number of objects the vehicle can carry. (You may need to consider both weight and volume.)
2. You are trying to determine a fee to charge customers for a single delivery. You plan to split the fee into two parts: a base rate and a distance rate.
   
   To determine the base rate, you plan to experiment with rational functions and determine two possible base rates, both based on the number of objects transported. Consider the following when determining your functions:
   
   • Decide on a minimum number of objects that will be transported at a time. Set your functions in such a way that a hole, or point of discontinuity, appears at the minimum number of objects for one function and an asymptote appears at the minimum number of objects for the other.
   • The capacity determined in question 1 will help you to determine the domain and range of your functions.
   • Rational functions can have various shapes. Experiment with a graphing calculator or graphing software using various degree polynomials in the numerator and denominator. Think about how you would like the rate to change as the person orders more items.
   • There are different ways for a function to measure the base rate. For example, it could determine the cost per item given the number of items or the total cost given the number of items. Be sure to explain what each function represents.
     
     
   Once you have decided on two functions, give a complete description of each one, including its graph, the general shape, where any non-permissible values occur, what occurs at the non-permissible values, and the domain and range for this scenario.
3. Use the functions you determined in question 2 to find the total base rate for three sizes of load. The following table may help organize your thinking:
   
   

   	Base Rate Using Function 1	Base Rate Using Function 2
   Order size = _______
   Order size = _______
   Order size = _______

4. 
   Ryan McVay/Photodisc/Thinkstock
   You are planning a promotional offer to entice customers to use your shipping business. For the next month, the first p objects are shipped for free with each load. Explain how this free shipping will affect each base rate by considering the following:
   • What value of p will you use?
   • What are the new base rate functions?
   • Is the offer better for large or small orders?
   • How reasonable will your offer be?
5. Pick a base rate function to use. Explain why you chose this rate and whether you feel a rational function was a good choice to begin with. What other type of function(s) would have made a good choice for determining a base rate? Explain why.

Part 2

 

Read all of Part 2 before beginning.

 

iStockphoto/Thinkstock

 

In this part you will use function operations to help determine functions related to your shipping business. You will determine a function related to shipping using each of the following:

• function addition
• function subtraction
• function multiplication
• function division
• composition of functions

For each function operation, provide the following:

• State what the functions before the operation represent and what the function after the operation represents. Explain why each function reasonably models what it is supposed to.
• At least three of your function operations must include explicit functions. For example, f(x) = 3x + 4 represents an explicit function, while f(x) represents a generic function.
• For each explicit function, show a sample calculation. (Imagine that you are explaining to a customer how the rule works.)
• Graph the initial and final functions on the same graph (if possible).
• Examples of some topics you may consider are taxes, discounts, fuel use, costs, currency exchanges, and load amounts.

Conclusion

Write a brief conclusion to your Module 7 Project. Include a personal reflection of what you feel you learned from the project during and after completion. Be sure to explain why you felt the way you did.

 

Assessment Guidelines

Your Module 7 Project will be evaluated by your teacher using the evaluation guidelines in the project rubric. Read the rubric carefully. Make sure you have completed the requirements for each of the categories. You can print or save a digital copy of the Module 7 Project Rubric as a guide to help you complete your project.

 

Don’t forget to submit your completed Module 7 Project to your teacher at the end of Module 7.