Business Decision Analysis, Homework
1. The Pinewood Furniture Company produces chairs and tables from two resources- labor and wood. The company has 80 hours of labor and 36 pounds of wood available each day. Demand for the chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 pounds of wood to produce, whereas a table requires 10 hours of labor and 6 pounds of wood. The profit derived from each chair is $400 and from each table $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.
2. A daily diet must be constructed determining the type and amount of foods to meet certain nutritional requirements at minimum cost. The foods that can be included are tuna fish, milk, spinach and whole-wheat bread; the nutrients we consider are vitamins A, C, and D, and iron. Nutritional and cost data are given in the table below.
|
Nutrient
|
Per Gallon of Milk
|
Per Pound of Tuna Fish
|
Per Loaf of bread
|
Per Pound of Spinach
|
Recommended daily allowance
|
|
Vitamin A
|
6,4000 IU
|
237 IU
|
0 IU
|
34,000 IU
|
5,000 IU
|
|
Vitamin C
|
40 mg
|
0 mg
|
0 mg
|
71 mg
|
75 mg
|
|
Vitamin D
|
540 IU
|
0 IU
|
0 IU
|
0 IU
|
400
|
|
Iron
|
28 mg
|
7 mg
|
13 mg
|
8 mg
|
12 mg
|
|
Cost
|
$1.95
|
$1.80
|
$0.75
|
$0.80
|
|
3. Gillian's Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week and has enough freezer space for 115 gallons total of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs $0.93 and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt( must make twice as much ice cream as frozen yogurt). Profit per gallon of ice cream is $4.15, and profit per gallon of yogurt is $3.60.
4. Ye Olde Winery in Peoria, Ill., makes three kinds of authentic German wine: Jeidelbery Sweet, Jeidelbery Rouge and Deutschland Extra Dry. The raw materials, labor and profit per liter of each wine is given in the tablebelow:
|
Wine
|
Grapes Grade A (kg)
|
Grapes Grade B (kg)
|
Sugar(kg)
|
Labor (hours)
|
Profit per Liter
|
|
Jeidelbery Sweet
|
1
|
1
|
2
|
2
|
1.00
|
|
Jeidelbery Rouge
|
2
|
0
|
1
|
3
|
1.20
|
|
Deutschland Extra Dry
|
0
|
2
|
0
|
1
|
2.00
|
The Winery has 150 kg of Grade A grapes, 150 kg of Grade B grapes, 80 kg of sugar and 225 hours of labor available during the next week. Formulate a linear programming model to determine the optimal product mix for Ye Olde Winery.
5. Two products can be produced on a certain machine. There are 12 hours of machine time to produce these products. Product 1 requires 60 minutes per unit and produce 2 requires half-an-hour per unit. Both products also require one raw material. Product 1 uses 4 pounds of raw material per unit and product 2 uses 3 pounds. There are 24 pounds of raw material available. Management has set a policy that requires twice as much Product 1 to be produced as Product 2. The goal is to maximize profit from these two products and product 1 contributes $4 per unit and product 2 contributes $5 per unit.
Formulate as LP to determine what quantity what quantity of each product should be produced.
6. Carlo's International manufactures blue jeans. Three brands are considered: A, B, and C. The manufacture of brand A requires 2 minutes machine time, 30 minutes labor, and costs $7. Brand B requires 2.5 minutes machine time, 40 minutes labor, and costs $10 to produce. Finally, brand C, the top of the line, requires 3 minutes machine time, 1 hour labor, and costs $13 to produce. Brand A sells for $12, brand B for $14, and brand C for $20.
The company works on a weekly schedule of five days, with two shifts of 7.5 hours per day. It has four machines available for production and 50 employees on each shift. The weekly manufacturing budget is $10,000. Its declared objective is profit maximization.