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76 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

between regular customers and new customers so that the total number of customers
contacted during the two-week period will be maximized. Technicians require an average of
50 minutes for each regular customer contact and one hour for each new customer contact.
a. Develop a linear programming model that will enable HTS to allocate technician time
between regular customers and new customers.
b. Find the optimal solution.
20 For the linear programme
Min 6x 1 þ 4x 2
s:t:
2x 1 þ 1x 2 12
1x 1 þ 1x 2 10
1x 2 4
x 1 ; x 2 0
a. Write the linear programme in standard form.
b. Find the optimal solution using the graphical solution procedure.
c. What are the values of the slack and surplus variables?
21 Consider the following linear programme:

Min 2x 1 þ 2x 2
s:t:
1x 1 þ 3x 2 12
3x 1 þ 1x 2 13
1x 1 1x 2 ¼ 3
x 1 ; x 2 0
a. show the feasible region.
b. what are the extreme points of the feasible region?
c. Find the optimal solution using the graphical solution procedure.

CASE PROBLEM 1 Workload Balancing

igital Imaging (DI) produces photo printers for lines to produce the printers. Line 1 performs the
D both the professional and consumer markets. assembly operation with times of three minutes per
The DI consumer division recently introduced two DI-910 printer and six minutes per DI-950 printer.
photo printers that provide colour prints rivalling Line 2 performs both the testing and packaging
those produced by a professional processing lab. operations. Times are four minutes per DI-910 printer
The DI-910 model can produce a 10cm 15cm and two minutes per DI-950 printer. The shorter time
borderless print in approximately 37 seconds. The for the DI-950 printer is a result of its faster print
more sophisticated and faster DI-950 can even pro- speed. Both manufacturing lines are in operation
duce a 35cm 50cm borderless print. Financial one eight-hour shift per day.
projections show profit contributions of $42 for each
DI-910 and $87 for each DI-950. Managerial Report
The printers are assembled, tested and pack-
Perform an analysis for Digital Imaging in order to
aged at DI’s plant located in Shanghai. This plant
determine how many units of each printer to pro-
is highly automated and uses two manufacturing
duce. Prepare a report to DI’s president presenting

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