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78 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

time, 450 hours of painting and finishing time and Managerial Report
140 hours of assembly, testing and packaging time
Analyze the production problem at Better Fitness,
will be available. Current labour costs are E20 per
Inc., and prepare a report for BFI’s president pre-
hour for machining and welding time, E15 per hour
senting your findings and recommendations. Include
for painting and finishing time and E12 per hour for
(but do not limit your discussion to) a consideration
assembly, testing and packaging time. The market in
of the following items:
which the two machines must compete suggests a
retail price of E2400 for the BodyPlus 100 and 1 What is the recommended number of BodyPlus
E3500 for the BodyPlus 200, although some flexibil- 100 and BodyPlus 200 machines to produce?
ity may be available to BFI because of the unique
2 How does the requirement that the number of
capabilities of the new machines. Authorized BFI
units of the BodyPlus 200 produced be at least
dealers can purchase machines for 70 per cent of
25 per cent of the total production affect profits?
the suggested retail price.
3 Where should efforts be expended in order to
BFI’s president believes that the unique capabil-
increase profits?
ities of the BodyPlus 200 can help position BFI as
one of the leaders in high-end exercise equipment.
Include a copy of your linear programming
Consequently, he has stated that the number of units
model and graphical solution in an appendix to your
of the BodyPlus 200 produced must be at least 25
report.
per cent of the total production.
CASE PROBLEM 3 Blending

local healthfood cooperative runs a community cafe´ and produces two vegetarian burgers. The large
A burger makes a profit of 85 cents per unit sold and the standard burger 55 cents. Each burger is made
from three basic ingredients as shown below. The cafe´ reckons it never sells more than a total of 100 burgers
in any one day (unsold burgers have to be thrown away for health reasons) but that it typically sells at least 30
of the standard burgers every day and 25 of the large.

Vegetable mix Soybean mix Crumb mix
Large burger 30 grams 150 grams 20 grams
Standard burger 30 grams 100 grams 20 grams
Availability 4 kilograms 10 kilograms 1.5 kilograms

Managerial Report

1 Provide a full explanation of the problem formulation for management (who have never heard of LP).
2 Provide management with advice as to what to do to maximize profit in this situation.
3 Advise management of the limitations of this analysis.

Provide model details and relevant computer output in a report appendix.

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