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142 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

Table 4.2 Manufacturing Times in Minutes Per Unit for Janders PDA
Components
Component Manufacturing Time

Base 1.0
Financial cartridge 3.0
Technician cartridge 2.5
Financial top 1.0
Technician top 1.5

the overtime premium cost rate of E9 per hour,wecan writetheobjective
function as:

Min 0:5BM þ 0:6BP þ 3:75FCM þ 4FCP þ 3:3TCM þ 3:9TCP þ 0:6FTM
þ 0:65FTP þ 0:75TTM þ 0:78TTP þ 9OT

The first five constraints specify the number of each component needed to satisfy the
demand for 3000 Financial Manager PDAs and 2000 Technician PDAs. A total of
5000 base components are needed, with the number of other components depending
on the demand for the particular calculator. The five demand constraints are:

BM þ BP ¼ 5000 Bases
FCM þ FCP ¼ 3000 Financial cartridges
TCM þ TCP ¼ 2000 Technician cartridges
FTM þ FTP ¼ 3000 Financial tops
TTM þ TTP ¼ 2000 Technician tops
Two constraints are needed to guarantee that manufacturing capacities for regular
time and overtime cannot be exceeded. The first constraint limits overtime capacity
to 50 hours, or:

OT 50
The same units of The second constraint states that the total manufacturing time required for
measurement must be all components must be less than or equal to the total manufacturing capacity,
used for both the left-
hand side and right-hand including regular time plus overtime. The manufacturing times for the compon-
side of the constraint. In ents are expressed in minutes, so we state the total manufacturing capacity con-
this case, minutes are straint in minutes, with the 200 hours of regular time capacity becoming
used.
60(200) ¼ 12 000 minutes. The actual overtime required is unknown at this point,
so we write the overtime as 60OT minutes. Using the manufacturing times from
Table 4.2, we have:

BM þ 3FCM þ 2:5TCM þ FTM þ 1:5TTM 12000 þ 60OT
Moving the decision variable for overtime to the left-hand side of the constraint
provides the manufacturing capacity constraint:

BM þ 3FCM þ 2:5TCM þ FTM þ 1:5TTM 60OT 12000

The complete formulation of the Janders make-or-buy problem with all decision
variables greater than or equal to zero is then:

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