 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

099

$36

100199

32

200299

30

300+

28

For
a price of $36, the optimal order quantity is ___________. (4)
2.
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

099

$36

100199

32

200299

30

300+

28

The optimal order quantity is
______________. (5)
4.
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
0100, with 100 being the most risky/liquid).
The various revenueproducing 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

Riskfree 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.
Riskfree 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. Formulate a linear program for ECU. DO NOT SOLVE THE LP. (10)
5.
Powers Tire Company (which specializes
in tires for vehicles ca. 1965) needs your expertise to help them schedule over
the next three months. They can make
tires using regular labor, overtime labor, or subcontracting. Their capacities (in tires) are as follows:
700/month for regular labor, 50/mo. for overtime labor, and 150/mo. for
subcontracted labor in March and April, and 130/mo. for subcontracted labor for
May. It costs $40/tire to produce with
regular labor, $50/tire with overtime, and $70/tire with subcontracting. It costs $2/tire/month to carry a tire in
inventory. Tires can be produced only
for the current or future periods, e.g., tires cannot be produced in May to fill
demand in April. Demands for the next
three periods are 800, 1000, and 750, for March, April, and May, respectively,
and all demand must be met. Check (or shade) all that apply. (12)
 This is an
integer program.
 This is a
transportation problem.
 The cost of
using regular labor in April to fill March demand is $40/tire.
 The cost of
using overtime labor in April to fill May demand is $52/tire.
 We would
need at least one dummy row.
 We would
need at least one dummy column.
6.
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)
1X11X2<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)
a. If this had been run as an integer program, we
would obtain a different solution.
(Check/shade if true.)
b. If
we could reduce the fat requirement by 100 lbs., the optimal solution would
change. (Check/shade if true.)
c. 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:
Change?
Increase?
d. 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:
We should be concerned.
Buckwheat?
Sunflower?
Poppy?
e. 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.
________________________