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202 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

CASE PROBLEM 2 Phoenix Computer

hoenix Computer manufactures and sells per- ber of students (new and current employees) that
P sonal computers directly to customers. Orders begin training each month cannot exceed 25.
are accepted by phone and through the company’s Phoenix needs to determine the number of new
website. Phoenix will be introducing several new lap- employees that should begin the three-month train-
top models over the next few months and manage- ing programme each month and the number of cur-
ment recognizes a need to develop technical sup- rent employees that should begin the two-month
port personnel to specialize in the new laptop training programme each month. The objective is
systems. One option being considered is to hire to satisfy staffing needs during May through Sep-
new employees and put them through a three-month tember at the lowest possible total cost; that is,
training programme. Another option is to put current minimize the incremental salary cost and the total
customer service specialists through a two-month training cost.
training programme on the new laptop models. It is currently January, and Phoenix Computer
Phoenix estimates that the need for laptop special- would like to develop a plan for hiring new employ-
ists will grow from 0 to 100 during the months of May ees and determining the mix of new and current
through September as follows: May – 20; June – 30; employees to place in the training programme.
July – 85; August – 85; and September – 100. After
September, Phoenix expects that maintaining a staff
Managerial Report
of 100 laptop specialists will be sufficient.
The annual salary for a new employee is esti- Perform an analysis of the Phoenix Computer prob-
mated to be E27 000 whether the person is hired lem and prepare a report that summarizes your find-
to enter the training programme or to replace a ings. Be sure to include information on and analysis
current employee who is entering the training pro- of the following items.
gramme. The annual salary for the current Phoenix
1 The incremental salary and training cost
employees who are being considered for the training
associated with hiring a new employee and
programme is approximately E36 000. The cost of
training him/her to be a laptop specialist.
the three-month training programme is E1500 per
2 The incremental salary and training cost
person, and the cost of the two-month training pro-
associated with putting a current employee
gramme is E1000 per person. Note that the length of
through the training programme. (Don’t forget
the training programme means that a lag will occur
that a replacement must be hired when the
between the time when a new person is hired and
current employee enters the programme.)
the time a new laptop specialist is available. The
number of current employees who will be available 3 Recommendations regarding the hiring and training
for training is limited. Phoenix estimates that the plan that will minimize the salary and training costs
following numbers can be made available in the over the February through August period as well as
coming months: March – 15; April – 20; May – 0; answers to these questions: What is the total cost of
June – 5; and July – 10. The training centre has the providing technical support for the new laptop
capacity to start new three-month and two-month models? How much higher will monthly payroll
training classes each month; however, the total num- costs be in September than in January?

CASE PROBLEM 3 Textile Mill Scheduling

he Shimla Textile Mill* in India produces five Table 4.18, along with data on the selling price per
T different fabrics for European clothing manu- metre, variable cost per metre and purchase price
facturers. Each fabric can be woven on one or more per metre. Prices are in euros. The mill operates 24
of the mill’s 38 looms. The sales department’s hours a day and is scheduled for 30 days during the
forecast of demand for the next month is shown in coming month.
*
This case is based on the Calhoun Textile Mill Case by Jeffrey D. Camm, P.M. Dearing, and Suresh K. Tadisnia, 1987.

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