In your own words, describe the special cases of integer programming and binary programming

This exercise consists of 2 short answer problems (no less than 400 words), and 4 linear programming problems. 

Question 1:

In your own words, describe the special cases of integer programming and binary programming: what makes these problems different? Give an example of each, pointing out why they must be an integer or binary programming problem as opposed to a standard linear programming problem.

Question 2

In your own words, describe how the linear programming process works. Your answer should demonstrate that you understand what a model is and how the optimization process works.

Question 3

Arizona Semiconductor is trying to determine which R&D projects to fund for the upcoming fiscal year. The company has a limit of $200,000 and 10 researchers available for R&D to be spread between several projects. The table below shows the resources required for each project for the upcoming year and the expected annual profit from each project.

	Project
1	2	3	4	5	6
Expense ($)	75	100	25	43	55	12
Number of Researchers	7	4	4	6	2	1
Profit ($)	92	85	4	72	50	15

1. Which projects should the company choose to maximize expected annual profit? How much is that profit? Set this up as a spreadsheet using Solver.

2. Suppose the company determines that that it must select either project 5 or 6 but not both. Does this change the list of projects the companies should undertake? How?

3. If the company wants to increase the amount of R&D it does in the upcoming year, should it allocate more funding or hire more researchers?

Question 4

Furrel’s Ice Cream Company ships ice cream in bulk from its manufacturing facility to its 25 retail outlets. Furrel’s has categorized its retail outlets into four types, each of which sells a certain level of ice cream per week, measured in pounds. Furrel’s ships its ice cream in two different size reusable containers: a 6-pound container and a 10-pound container. The company currently has 200 6-pound containers and 25 10-pound containers. The company would like to minimize the amount of excess ice cream shipped to each store while making use of its existing reusable containers. For example, store type 1 needs 25 pounds of ice cream a week. Furrel’s could ship this in one 10-pound container and three 6-pound containers for a total of 28 pounds (3 pounds excess) or in two 10-pound containers and one 6-pound containers (1 pound excess). However, with only 25 10-pound containers available, it is not clear that this is the best choice for this type of store.

	Store Type
Type 1	Type 2	Type 3	Type 4
Pounds of Ice Cream needed	25	40	50	100
Number of Stores	10	5	4	6

1. Given this current store configuration and the number of reusable containers available, how many 6-pound and 10-pound containers should be used to ship to each store in order to minimize the excess ice cream? How much excess ice cream will this lead to each week?

2. Should Furrel’s purchase more 6-pound containers or more 10-pound containers? Why?

Question 5

The AppleBerry Company has three warehouses where it stores its tablet computer devices and four distributors that place these products in retail stores and online. Each warehouse holds 5000 devices. Because of the various distances between the warehouses and the distribution centers, there are different costs to ship the devices from each warehouse to each distributor. The cost per device for shipping between the warehouses and distributors is given in the table below. Additionally, each distributor has calculated an estimated monthly demand for the tablet and does not want to receive any more tablets than this estimated demand.

From	To
	Dist 1	Dist 2	Dist 3	Dist 4
Whse A	$8	$10	$6	$3
Whse B	$9	$15	$8	$6
Whse C	$5	$12	$5	$7

Distributor	Estimated Monthly Demand
1	2500
2	2500
3	2000
4	3500

1. Given these facts, how many devices should be shipped from each warehouse to each distributor per month, in order for AppleBerry to minimize its costs? What is this minimized cost? Set this up as a spreadsheet using Solver.

2. AppleBerry is looking to shut down one of its warehouses. In your opinion, based on this model, which warehouse should be shut down? Explain your answers.

Question 6

The AppleBerry Company makes a mix of three types of electronic devices: MP3 players, eReaders, and tablet computers. The company is trying to determine which products to make to optimize its profits. Each product requires a specific number of hours in fabrication, assembly, and machining. In addition, to save on expenses, all the devices have been engineered to use the same basic raw materials. The table below details the hours and costs involved, as well as the profit per device. AppleBerry has a total of 2000 hours of fabrication, 3200 hours of assembly, and 1600 hours of machining currently available per month. It also has budgeted to purchase $9200 of raw materials each month.

Device	Fabrication Hours Required	Assembly Hours Required	Machining Hours Required	$ of raw Materials Needed	Profit per Device
MP3 Player	6	6	9	$30	$16
eReader	6	8	6	$40	$20
Tablet	2	12	8	$25	$14

Answer the following questions:

1. Given the current situation, what product mix should AppleBerry use to maximize its monthly profits? What is the optimized monthly profit? Set this up as a spreadsheet using Solver.

2. If AppleBerry chooses to commit more resources to increase profits, should it purchase more fabrication time, assembly time, machining time, or raw materials?