D.4 Computer Analysis
1) The simplex method is an interactive algebraic procedure for solving linear programming problems.
2) The simplex method deals exclusively with corner points
3) Degeneracy occurs when the linear program model consists of only an infeasible region.
4) ________ occurs in a linear programming problem when the number of nonzero variables in the
optimal solution is fewer than the number of constraints.
5) What is degeneracy in the context of linear programming? Why is degeneracy a concern?
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D.5 The Transportation Method
Table D.1
Tanfastic, Inc., a manufacturer of swimwear, is in the process of developing a production plan for the
coming spring break. The ending inventory for January is 30 units. Undertime is paid, at a rate of $5.00
per unit. Details are shown in the following POM for Windows table.
1) Use the information in Table D.1. Given the information in the optimal tableau, what is the inventory
carrying cost, in dollars per unit per quarter?
A) less than $1
B) greater than $1 but less than or equal to $2
C) greater than $2 but less than or equal to $3
D) greater than $3
2) Use the information in Table D.1. Given the information in the optimal tableau, what is the overtime
cost in dollars per unit?
A) less than $12
B) greater than $12 but less than or equal to $14
C) greater than $14 but less than or equal to $16
D) greater than $16
Table D.2
Bahouth Enterprises produces a variety of hookahs for clients around the globe. Their small plant has a
highly flexible workforce that can switch between products seamlessly. They forecast using a six-month
planning period and have a demand forecast as shown in the table. The per-unit costs for each output
option the sales and operations planner has at his disposal are indicated in the table. Regular output costs
$40 per unit, overtime production is $60 per unit, and subcontracting is $70 per unit. Holding inventory
from one month to the next costs $2 per unit per month and a backlog costs $5 per unit per month.
Regular plant capacity is 300 units per month.
Period
1
2
3
4
5
6
Total
Forecast
400
350
500
400
500
200
2,350
Output
Regular
$40
1,800
Overtime
$60
0
Subcontract
$70
0
Inventory
Beginning
0
Ending
$2
Average
0
Backlog
$5
2,250
Costs
3) Use the information in Table D.2. If the planner decides to adopt a chase plan for the planning period,
what will the regular output be for month 1?
A) 300 units
B) 350 units
C) 400 units
D) 450 units
4) Use the information in Table D.2. If the planner decides to adopt a level plan for the planning period,
what will the total output be for month 3?
A) between 350 and 400 units
B) between 400 and 450 units
C) between 450 and 500 units
D) more than 500 units
5) Use the information in Table D.2. If the planner decides to adopt a level plan for the planning period,
what will the regular output be for month 3?
A) between 290 and 330 units
B) between 330 and 370 units
C) between 370 and 410 units
D) between 410 and 450 units
6) Use the information in Table D.2. If the plant has no limits on the number of units produced by
overtime or subcontractors, what is the lowest-cost chase plan that is possible for the six-month period?
A) less than $50,000
B) between $50,000 and $100,000
C) between $100,000 and $150,000
D) between $150,000 and $200,000
7) Use the information in Table D.2. The plant has no limits on the number of units produced by overtime
or subcontractors and adopts a chase plan strategy for the six-month planning period. What is the cost for
month 6 of their chase plan?
A) $8,000
B) $9,852
C) $11,317
D) $12,631
8) Use the information in Table D.2. The plant has no limits on the number of units produced by overtime
or subcontractors and adopts a level plan strategy for the six-month planning period. What is the cost for
month 6 of their level plan?
A) between $16,200 and $16,600
B) between $16,600 and $17,000
C) between $17,000 and $17,400
D) between $17,400 and $17,800
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Table D.3
The Harper Company is in the process of production planning for the next four quarters. The company
follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted
demand. Anticipation inventory is also allowed, but not backorders. Undertime is paid, at a rate of $5.00
per unit. The beginning (or current) inventory is 25 units. Details are shown in the following POM for
Windows table.
9) Use the information in Table D.3. What is the total cost of the optimal production plan?
A) less than or equal to $1,000
B) greater than $1,000 but less than or equal to $2,000
C) greater than $2,000 but less than or equal to $3,000
D) greater than $3,000
10) Use the information in Table D.3. What is the anticipation inventory at the end of the first quarter?
A) 0 units
B) 1 through 5 units
C) 6 through 10 units
D) 11 units and above
11) Use the information in Table D.3. According to the optimal production plan, what is the total ending
inventory in the second quarter? Assume that the plan that uses the least amount of subcontracting is
used.
A) none
B) two units
C) three units
D) greater than three units
12) Use the information in Table D.3. According to the optimal production plan, what is the overtime
production in the second quarter?
A) two units
B) three units
C) four units
D) five units
13) Use the information in Table D.3. Given the information in the optimal tableau, what is the demand
forecast for quarter 2?
A) fewer than 30 units
B) greater than 30 units but fewer than or equal to 35 units
C) greater than 35 units but fewer than or equal to 40 units
D) greater than 40 units
14) Use the information in Table D.3. Given the information in the optimal tableau, what is the inventory
carrying cost, in dollars per unit per quarter?
A) less than $1
B) greater than $1 but less than or equal to $2
C) greater than $2 but less than or equal to $3
D) greater than $3
15) Use the information in Table D.3. Given the information in the optimal tableau, what is the
subcontracting cost, in dollars per unit?
A) $5
B) $7
C) $10
D) $12
16) Provide three examples of operations management decision problems for which linear programming
can be useful, and why.
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17) A snack food producer runs four different plants that supply product to four different regional
distribution centers. The division operations manager is focused on one product, so he creates a table
showing each plant’s monthly capacity and each distribution center’s monthly demand (both amounts in
cases) for the product. The division manager supplements this table with the cost data to ship one case
from each plant to each distribution center. Formulate an objective function and constraints that will
solve this problem using linear programming.
Center 2
Center 4
Monthly
Capacity
Plant A
$7
$4
8,000
Plant B
$4
$6
12,000
Plant C
$6
$3
7,500
Plant D
$8
$5
5,000
Monthly
Demand
8,500
7,000
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Answer: This is a cost minimization problem with 16 decision variables, one for each combination of
plant and center; there are 8 constraints, one for each plant’s capacity and one for each center‘s demand.
Objective Min Z = $2xA1 + $7xA2 + $5xA3 + $4xA4 + $9xB1 + $4xB2 + $7xB3 + $6xB4 + $7xC1 + $6xC2 +
$4xC3 + $3xC4 + $4xD1 + $8xD2 + $3xD3 + $5xD4