3.Arizona Semiconductor is trying to determine the best place to build a manufacturing plant. Arizona wants it to be centrally located between six of its assembly facilities. These assembly facilities are mapped on a two-dimensional grid using x,y coordinates as follows:
|
Facility
|
x
|
y
|
|
1
|
12
|
101
|
|
2
|
33
|
42
|
|
3
|
22
|
75
|
|
4
|
38
|
82
|
|
5
|
24
|
69
|
|
6
|
35
|
48
|
Where should the new manufacturing plant be built in order to minimize the distance between all the assembly facilities? The answer should be an x,y coordinate. Use the formula to determine the distance between the new plant and an assembly facility, where x,y represents the location of the new plant and represents the location of any particular assembly facility.
4. 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
|
- Which projects should the company choose to maximize expected annual profit? How much is that profit? Set this up as a spreadsheet using Solver.
- 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?
- 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?
5. 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:
- 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.
- If AppleBerry chooses to commit more resources to increase profits, should it purchase more fabrication time, assembly time, machining time, or raw materials?
6. Snoo Coffee Company creates three blends of coffee: budget, classic, and premium. The coffee blends are composed of four ingredients: A, B, C, and D. The table below shows the percentage of each component that are in each blend and the cost per pound for that ingredient. The blends have a wholesale price of $2.50, $3.00, and $4.50 for budget, classic, and premium, respectively. A limited amount of each ingredient is available on a weekly basis.
|
Ingredient
|
Budget
|
Classic
|
Premium
|
Cost/lb.
|
Max Weekly Availability
|
|
A
|
25%
|
35%
|
0%
|
$0.60
|
40,000
|
|
B
|
55%
|
25%
|
0%
|
$0.80
|
20,000
|
|
C
|
5%
|
10%
|
50%
|
$0.95
|
35,000
|
|
D
|
15%
|
30%
|
50%
|
$0.70
|
45,000
|
Snoo can make 100,000 pounds of coffee per week, and it wants to make a minimum of 25,000 pounds of each blend. (20 points)
- In order to maximize weekly profits, how many pounds of each ingredient should be purchased?
- What is the shadow price of ingredient C?
- How much should Snoo be willing to pay for an additional pound of ingredient C to raise total profit?