Final Project

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Eastern Gateway Community College *

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105

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Mechanical Engineering

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Dec 6, 2023

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1 Final Project Jordan Brown Central State University Quantitative Meth. For Manager Dr. Saima Bashir November 30, 2023

2 Final Project 1. The recommended number of BodyPlus 100 and BodyPlus 200 machines to produce. Components and requirements for the BodyPlus 100 & 200 models: Machining and Welding Time(s) Frame Press Station Pec-Dec Station Leg-Press Station Total BodyPlus 100 4 Hrs 2 Hrs 2 Hrs N/A 8 Hrs BodyPlus 200 5 Hrs 3 Hrs 2 Hrs 2 Hrs 12 Hrs Painting and Finishing Time(s) Frame Press Station Pec-Dec Station Leg-Press Station Total BodyPlus 100 2 Hrs 1 Hr 2 Hrs N/A 5 Hrs BodyPlus 200 4 Hrs 2 Hrs 2 Hrs 2 Hrs 10 Hrs  BodyPlus 100: $450/frame, $300/press station, $250/pec-dec station, $50/packaging  BodyPlus 200: $650/frame, $400/press station, $250/pec-dec station. $200/leg-press station, $75/packaging  600 Hrs for machining & welding; 450 Hrs for painting and finishing; 140 Hrs for assembly, testing, and packaging  Additional 2 Hrs for assembly, testing, and packaging each machine  Labor: $20/hr machining and welding; $15/hr painting and finishing; $12/hr assembly  Selling points: Model100 = $2400; Model 200 = $3500  Model100: 2400 – (450+300+250+50-259) = 2400 – 1309 - $1,091  Model200: 3500 – (650+400+250+200+75+414) = 3500 – 1999 = $1,511 o 2400*0.7=$1,680; 3500*0.7=$2,450 o 1680-1309=$371; 2450-1999=$461  (Machining and welding): 8Model100 + 12Model200 <= 600  (Painting and finishing): 5Model100 + 10Model200 <= 450  (Assembly, testing, and packing): 2Model100 + 2Model200 <= 140  (Model200 Minimum): 0.25Model100 – 0.75Model200 <= 0  (Non-negative): Model100, Model200 >=0

3 o This results in 50 Model 100s and 17 Model 200s, giving a max profit of $26,2333.33  (Machining and welding): 8Model100 + 12Model200 <= 600  (Painting and finishing): 5Model100 + 10Model200 <= 450  Assembly, testing, and packing): 2Model100 + 2Model200 <= 140  (Non-negative): Model100, Model200 >=0 o This results in 60 Model 100s and 10 Model 200s, giving a max profit of $26,870.00 When the 25% minimum is eliminated, an overall higher profit can be found by creating 60 Model 100s and 10 Model 200s. When keeping the 25% minimum of Model 200s in production, profits are slightly hampered, but optimized at 50 Model 100s and 17 (16.67 rounded up) Model 200s. 2. The effect on profits of the requirement that the number of units the BodyPlus 200 produced must be at least 25% of the total production. With the requirement being at least 25% of the total production needing to be BodyPlus 200 model machines, potential profits are missed. When sticking to this requirement, the maximum optimal output is 17 Model200s and 50 Model 100s; thus, resulting in $26,333.33 profit. When the 25% minimum requirement is removed, the company can shift its production to true optimization; this being 10 Model200s and 60 Model100s. The profits increase further to $26,870. The difference is $636.67 is possible profits lost/unrealized (26870-26333.33=$636.33). 3. Where efforts should be expanded in order to increase contribution to profits.

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4 In order to increase contributions to profits, the company could forego the 25% minimum requirement of for Model200s as this causes additional potential profits to be missed. However, keeping the 25% requirement reflects machining and welding being fully utilized. If the 25% minimum requirement is held, there could be an increase to both machining and welding times to help. This, in turn, would help profits over time, while also utilizing the excess slack from painting, finishing, assembly, testing, and packaging.  8(50) + 12(16.667) = 600.004 (Rounded to 600) (Machining and Welding)  5(50) + 10(16.667) = 416.67; 460-416.67=33.33 hours of slack  2(50) + 2(16.667) = 133.334; 140-133.334=6.666 hours of slack Increases to machining and welding and optimize the other areas of production, leading to higher future profits (though sub-optimal profits in the short-run).