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GENERAL LINEAR PROGRAMMING NOTATION 77

your findings and recommendations. Include (but do 4 Management requested an expansion of the
not limit your discussion to) a consideration of the model in part (2) that would provide a better
following: balance between the total time on line 1 and the
total time on line 2. Management wants to limit
1 The recommended number of units of each the difference between the total time on line 1 and
printer to produce to maximize the total the total time on line 2 to 30 minutes or less. If the
contribution to profit for an eight-hour shift. What objective is still to maximize the total contribution
reasons might management have for not to profit, how many units of each printer should
implementing your recommendation? be produced? What effect does this workload
2 Suppose that management also states that the balancing have on total profit in part (2)?
number of DI-910 printers produced must be at 5 Suppose that in part (1) management specified
least as great as the number of DI-950 units the objective of maximizing the total number of
produced. Assuming that the objective is to printers produced each shift rather than total
maximize the total contribution to profit for an profit contribution. With this objective, how many
eight-hour shift, how many units of each printer units of each printer should be produced per
should be produced? shift? What effect does this objective have on
3 Does the solution you developed in part (2) total profit and workload balancing?
balance the total time spent on line 1 and the total For each solution that you develop include a copy of
time spent on line 2? Why might this balance or your linear programming model and graphical solu-
lack of it be a concern to management? tion in the appendix to your report.

CASE PROBLEM 2 Production Strategy

etter Fitness, Inc. (BFI), manufactures exercise each pec-dec station uses two hours of machining
B equipment at its plant in Munich, Germany. It and welding time and two hours of painting and finish-
recently designed two universal weight machines ing time. In addition, two hours are spent assembling,
for the home exercise market. Both machines use testing and packaging each BodyPlus 100. The raw
BFI-patented technology that provides the user with material costs are E450 for each frame, E300 for each
an extremely wide range of motion capability for press station and E250 for each pec-dec station;
each type of exercise performed. Until now, such packaging costs are estimated to be E50 per unit.
capabilities have been available only on expensive The BodyPlus 200 consists of a frame unit, a press
weight machines used primarily by physical thera- station, a pec-dec station and a leg-press station. Each
pists. frame produced uses five hours of machining and weld-
At a recent trade show, demonstrations of the ing time and four hours of painting and finishing time.
machines resulted in significant dealer interest. In Each press station requires three hours machining and
fact, the number of orders that BFI received at the welding time and two hours of painting and finishing
trade show far exceeded its manufacturing capabil- time, each pec-dec station uses two hours of machin-
ities for the current production period. As a result, ing and welding time and two hours of painting and
management decided to begin production of the two finishing time, and each leg-press station requires two
machines. The two machines, which BFI named the hours of machining and welding time and two hours of
BodyPlus 100 and the BodyPlus 200, require differ- painting and finishing time. In addition, two hours are
ent amounts of resources to produce. spent assembling, testing and packaging each Body-
The BodyPlus 100 consists of a frame unit, a press Plus 200. The raw material costs are E650 for each
station and a pec-dec station. Each frame produced frame, E400 for each press station, E250 for each
uses four hours of machining and welding time and pec-dec station and E200 for each leg-press station;
two hours of painting and finishing time. Each press packaging costs are estimated to be E75 per unit.
station requires two hours of machining and welding For the next production period, management esti-
time and one hour of painting and finishing time, and mates that 600 hours of machining and welding

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