Question 1:
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
|
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)
1. In order to maximize weekly profits, how many pounds of each ingredient should be purchased?
2. What is the shadow price of ingredient C?
3. How much should Snoo be willing to pay for an additional pound of ingredient C to raise total profit?
Question 2:
The Canadian Motorcycle Company (CMC) has determined that its customers are very price-sensitive, with the number of motorcycles purchased heavily dependent upon the prices set. The company makes two different styles of bike: the high-end "Jet" and the lower-end "Canuck." Market research has shown that the Jet has a price-demand curve of p = 22,000 - 0.25x, where p represents price and x represents the demand volume. For the Canuck, the curve is p = 18000 - 0.3x. In order to determine profit, CMC will simply take the selling price minus the materials costs. Raw materials for the Jet are $6000 per bike, and they are $5000 per bike for the Canuck. Since CMC hand-builds each bike it makes, the only real constraint for building the bike is the number of manufacturing hours available. CMC has 10,000 hours per month of manufacturing capacity available. A Jet takes 23 hours to manufacture and a Canuck takes 20. CMC also wants to ensure the integrity of each product line, so it will require that a minimum of 100 of each bike should be made each month. Note: All figures are in Canadian dollars.
1. How many of each type of bike should CMC manufacture each month? What will its profit be?
2. Should it drop its minimum limit of 100 of each bike? Why or why not?
Question 3:
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?
Question 4:
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.