1. Better Fitness, Inc. (BFI), manufactures exercise equipment at its plant in Freeport, Long
Island. It recently designed two universal weight machines for the home exercise market.
Both machines use BFI-patented technology that provides the user with an extremely wide
range of motion capability for each type of exercise performed. Until now, such capabilities
have been available only on expensive weight machines used primarily by physical therapists.
At a recent trade show, demonstrations of the machines resulted in significant dealer interest.
In fact, the number of orders that BFI received at the trade show far exceeded its manufacturing capabilities for the current production period. As a result, management decided to
begin production of the two machines. The two machines, which BFI named the BodyPlus
100 and the BodyPlus 200, require different amounts of resources to produce.
The BodyPlus 100 consists of a frame unit, a press station, and a pec-dec station. Each
frame produced uses 4 hours of machining and welding time and 2 hours of painting and
finishing time. Each press station requires 2 hours of machining and welding time and 1 hour
of painting and finishing time, and each pec-dec station uses 2 hours of machining and welding
time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling,
testing, and packaging each BodyPlus 100. The raw material costs are $450 for each frame,
$300 for each press station, and $250 for each pec-dec station; packaging costs are estimated
to be $50 per unit.
The BodyPlus 200 consists of a frame unit, a press station, a pec-dec station, and a leg-press
station. Each frame produced uses 5 hours of machining and welding time and 4 hours of
painting and finishing time. Each press station requires 3 hours of machining and welding time
and 2 hours of painting and finishing time, each pec-dec station uses 2 hours of machining and
welding time and 2 hours of painting and finishing time, and each leg-press station requires 2
hours of machining and welding time and 2 hours of painting and finishing time. In addition,
2 hours are spent assembling, testing, and packaging each BodyPlus 200. The raw material
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costs are $650 for each frame, $400 for each press station, $250 for each pec-dec station, and
$200 for each leg-press station; packaging costs are estimated to be $75 per unit.
For the next production period, management estimates that 600 hours of machining and
welding time, 450 hours of painting and finishing time, and 140 hours of assembly, testing,
and packaging time will be available. Current labor costs are $20 per hour for machining and
welding time, $15 per hour for painting and finishing time, and $12 per hour for assembly,
testing, and packaging time. The market in which the two machines must compete suggests
a retail price of $2400 for the BodyPlus 100 and $3500 for the BodyPlus 200, although some
flexibility may be available to BFI because of the unique capabilities of the new machines.
Authorized BFI dealers can purchase machines for 70% of the suggested retail price.
BFI’s president believes that the unique capabilities of the BodyPlus 200 can help position
BFI as one of the leaders in high-end exercise equipment. Consequently, he has stated that the
number of units of the BodyPlus 200 produced must be at least 25% of the total production.
Managerial Report
(a) What is the recommended number of BodyPlus 100 and BodyPlus 200 machines to
produce?
(b) How does the requirement that the number of units of the BodyPlus 200 produced be
at least 25% of the total production affect profits?
(c) Where should efforts be expended in order to increase profits?
2. Cloud Services Capacity Planning. Galaxy Cloud Services operates several data centers
across the United States containing servers that store and process the data on the Internet.
Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in
Michigan, Ohio, and California and two in New York. Management is considering increasing
the capacity of these data centers to keep up with increasing demand. Each data center
contains servers that are dedicated to Secure data and to Super Secure data. The cost to
update each data center and the resulting increase in server capacity for each type of server
are as follows:
Data center Cost($millions) Secure Servers Super Secure Servers
Michigan 2.5 50 30
New York 1 3.5 80 40
New York 2 3.5 40 80
Ohio 4 90 60
California 2 20 30
The projected needs are for a total increase in capacity of 90 Secure servers and 90 Super
Secure servers. Management wants to determine which data centers to update to meet projected needs and, at the same time, minimize the total cost of the added capacity.
In particular you have been asked to
(a) Formulate a binary integer programming model that could be used to determine the
optimal solution to the capacity increase question facing management.
(b) Solve the model formulated in part (a) to provide a recommendation for management.
