Reference no: EM132713249
Question 1:
A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return.
|
Bond
|
Annual Return
|
Maturity
|
Risk
|
Tax
Free
|
|
A
|
9.5%
|
Long
|
High
|
Yes
|
|
B
|
8.0%
|
Short
|
Low
|
Yes
|
|
C
|
9.0%
|
Long
|
Low
|
No
|
|
D
|
9.0%
|
Long
|
High
|
Yes
|
|
E
|
9.0%
|
Short
|
High
|
No
|
The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free.
1. Formulate the LP model for this problem.
2. Create the spreadsheet model and use Solver to solve the problem.
Question 2:
Tuckered Outfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50 and $3.00 per pound. The vitamin, mineral, and protein content of each of the ingredients (in grams per pound) is summarized in the following table along with the calories per pound of ingredient:
|
|
Raisins
|
Grain
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Chocolate Chips
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Peanuts
|
Almonds
|
|
Vitamins
|
20
|
10
|
10
|
30
|
20
|
|
Minerals
|
7
|
4
|
5
|
9
|
3
|
|
Protein
|
4
|
2
|
1
|
10
|
1
|
|
Calories
|
450
|
160
|
500
|
300
|
500
|
The company would like to identify the least costly mix of these ingredients that provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein, and 600 calories per 2-pound package. Additionally, they want each ingredient to account for at least 5% and no more than 50% of the weight of the package.
1. Formulate the LP model for this problem.
2. Create the spreadsheet model and use Solver to solve the problem.
3. What is the optimal mix, and how much is the total ingredient cost per package?
Question 3:
7-22 The load master for a freighter wants to determine the mix of cargo to be carried on the next trip. The ship's volume limit for cargo is 100,000 cubic meters. and its weight capacity is 2,310 tons. The master has five different types of cargo from which to select and wishes to maximize the value of the selected shipment. However, to make sure that none of his customers are ignored. the load master would like to make sure that at least 20% of each cargo's available weight is selected. The specifications for the five cargoes are shown in the following table.
|
CARGO
|
TONS
|
VALUE
|
VOLUME PER
|
|
TYPE
|
AVAILABLE
|
PER TON
|
TON (cu. st.)
|
|
A
|
970
|
$1,350
|
26
|
|
B
|
850
|
$1,675
|
54
|
|
C
|
1.900
|
$1.145
|
28
|
|
D
|
2.300
|
$ 850
|
45
|
|
E
|
3.600
|
$1,340
|
37
|
|
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