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Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity
Price/pair
0-125
$37
126-225
35
226-350
33
351+
31
For a price of $37, the optimal order quantity is ___________. (4)
- Redo #1 if they allow backordered items with a shortage cost of $4/quarter.
Optimal order quantity = ___________. (4)
Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity
Price/pair
0-125
$37
126-225
35
226-350
33
351+
31
The optimal order quantity is ______________. (5)
The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year. ECU makes four types of loans and has three additional investment instruments. Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-100, with 100 being the most risky/liquid). The various revenue-producing instruments are summarized in the table below:
Instrument
Annual Rate of Return (%)
Risk Factor
Liquidity Factor
Automobile loans
8
50
0
Furniture loans
10
60
0
Other secured loans
11
70
0
Unsecured loans
14
80
0
Risk-free securities
5
0
100
Corporate stock fund
9
60
90
Corporate bond fund
8
50
80
ECU has $2,000,000 available for investment during the coming year. However, state laws and pesky stakeholders impose certain restrictions on choice of investment instruments. Risk-free securities may not exceed 30% of total funds available for investment. Unsecured loans may not exceed 10% of total funds invested in loans. The funds invested in automobile loans must not be less than the total of funds invested in furniture and other secured loans. The average risk factor may not exceed 60, and the average liquidity factor must be at least 40. Check all that apply.
- We are required to invest a total of $2,000,000.
- There are 7 decision variables.
- There are 6 constraints (not including nonnegativity).
- 0 is a right hand side value.
- 60,000 is a right hand side value.
- The average risk factor is (50 + 60 + 70 + 80 + 0 + 60 + 50)/7.
- You are asked to assign four patients to five nurses using the following travel distances. We want to minimize total mileage. (10)
Patient
Nurse
Warren
Xavier
Yolanda
Zanthia
Amy
20
25
15
12
Brenda
15
18
27
20
Connor
32
22
17
23
Danielle
41
16
12
28
Emily
24
29
19
16
- As a linear program, there are twenty-five decision variables.
- In the optimal solution, Danielle is assigned to Yolanda.
- The optimal total mileage is 55.
- If we added a fifth patient, she would be assigned to Emily.
- This is a transportation problem.
Hungry Birds, Inc. manufactures birdseed. One variety consists of wheat. They are trying to determine the optimal mix of buckwheat (X1), sunflower (X2), and poppy (X3) (each in lbs.). Relevant information is provided in the following table. In addition, the final mix is required to contain at least 500 lbs. of poppy. Also, the total weight of the buckwheat may not exceed the total weight of the sunflower in the final mix.
Nutritional Item
Proportional Content
Total Requirement
Buckwheat
Sunflower
Poppy
Fat
0.04
0.06
0.05
480
Protein
0.12
0.10
0.10
1200
Roughage
0.10
0.15
0.07
1500
Cost/lb.
$0.18
$0.10
$0.11
The output of the linear program is given on the following page.
LINEAR PROGRAMMING PROBLEM
MIN 0.18X1+0.1X2+0.11X3
S.T.
1) .04X1+.06X2+.05X3>480
2) .12X1+.1X2+.1X3>1200
3) .1X1+.15X2+.07X3<1500
4) 1X3>500
5) 1X1-1X2<0
OPTIMAL SOLUTION
Objective Function Value = 1237.500
Variable Value Reduced Costs
-------------- --------------- ------------------
X1 0.000 0.050
X2 8250.000 0.000
X3 3750.000 0.000
Constraint Slack/Surplus Dual Prices
-------------- --------------- ------------------
1 202.500 0.000
2 0.000 -1.188
3 0.000 0.125
4 3250.000 0.000
5 8250.000 0.000
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
X1 0.130 0.180 No Upper Limit
X2 No Lower Limit 0.100 0.110
X3 0.100 0.110 0.160
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
1 No Lower Limit 480.000 682.500
2 1026.667 1200.000 2142.857
3 840.000 1500.000 1760.000
4 No Lower Limit 500.000 3750.000
5 -8250.000 0.000 No Upper Limit
(15)
If this had been run as an integer program, we would obtain a different solution. (Check/shade if true.)If we could reduce the fat requirement by 100 lbs., the optimal solution would not change. (Check/shade if true.)A new customer wants a mix with at least 20% buckwheat. Would this change the optimal solution? If so, would it increase or decrease? Check/shade the following: Nora in Accounting noted a glitch in her software, and stated that the cost estimates should be changed. She said the cost values should be $0.17 for buckwheat, $0.12 for sunflower, and $0.12 for poppy. Would this be a cause for concern? If so, which component(s) would be affected? Check/shade the following:If you could relax the requirement on one nutritional item, which would be the best choice to achieve the lowest cost? Fill in the blank.
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