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Kelvin Shoe Stores carries a basic black dress shoe | Complete Solution
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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

 

  1. As a linear program, there are twenty-five decision variables.

 

  1. In the optimal solution, Danielle is assigned to Yolanda.

 

  1. The optimal total mileage is 55.

 

  1. If we added a fifth patient, she would be assigned to Emily.

 

  1. 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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Kelvin Shoe Stores carries a basic black dress shoe | Complete Solution
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  • Submitted On 27 Apr, 2015 10:07:41
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EOQ = sqrt (2*(500*4)*30/(0.2*37)) = 127.34 = 127 units As, for $37, only 0-125 can be ordered. So...
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