The Holiday Transportation Side Job Let us apply some of the concepts we have learned in the previous two chapters regarding systems of equations, inequalities, and linear programming. By this time, the student should be aware of the importance of setting up and solving a system of equations and inequalities, not to mention the importance of linear programing as a tool in solving real life problems related to resource allocation and linear optimization. Note: Real life Linear Programing problems require many inequalities not to mention variables....and as you read the hypothetical problem listed below you will clearly notice that there are many many variables you might need to consider to run a successful business so for that reason we will keep it simple ok. Hypothetical: During the Holidays, many transportation companies cannot keep-up with the high demand of e-commerce and consumers' purchases. After making a few phone calls and several meetings around the RGV area you see an opportunity to start your own delivery business. A family member has a cargo van that you can use so you have a delivery vehicle. Later in the week, you have secured a contract where you would pick-up items from a warehouse and take them to a local store. The customers would then receive a notification that their order is ready for pick-up. To make sure you optimize the use of the delivery van you need to do a few basic calculations starting with how much you can carry/load. Your cargo van can carry no more than 800 pounds of cargo and no more than 125 cubic feet of cargo. Luckily, the warehouse has only two types of packages. Small packages weigh 8 pounds and occupies
0.5
cubic feet of space. And large packages that weigh 20 pounds and occupies 5 cubic feet of space. Create a Word document or a PDF file that will answer the following questions. a) Using the variable
x
to represent the number of small packages and the variable
y
to represent the number of large packages write a system of linear inequalities that can describe the number of packages you can carry in your van. b) Graph the system of inequalities using Desmos or a graphing utility; Label all the corner points of your graph. (Note: Copy/Paste graph and make sure it is included in the document you submit to your instructor. c) How much will you make? Well,
$150
per day plus
$2
dollars per every small package transported and
$6
per every large package transported. Write an equation that describes the amount of money you will receive every day. How much money will you receive if you transport 25 small packages and 15 large packages? d) Given the information provided, what is the maximum amount of money you could make? Justify your answer and describe how you arrived at your answer.
