One page analysis of the output related to the problem. The following questions should be answered in the analysis.
What is the objective function value? What does this value mean in context of the problem?
What is the optimal solution? What does it mean for Colt manufacturing?
What does the slack/surplus value tells us in this problem? What does dual value specifically tell us about this problem?
What does the Objective Function ranges and Right Hand Side Ranges tells us in this problem?
What overall recommendations would you make to Colt Manufacturing and their goal to maximize profit?
Colt manufacturing have selected five products they can produce utilizing ABS and PLA 3D printing methods. Shawshank Executive Decisions, LLC have been asked to decide how many and which types butt stocks or hand grips they can produce in order to maximize profit for the company. The sales team has determined that the company stand to profit $3 from conventional butt stocks, $4 from hand grips, $6 from forward hand grips, $8 form colt cobra grip and $10 from M16 A1 Retro butt stocks. The marketing and operations department have identified some limitations.
1. Only 60 hours of labor time is allowed each day.
2. Machine allows only 80 hours of run time each day.
3. No more than 50 of all hand grips must be produced.
4. We must produce at least 30 Colt cobra grip per day.
5. Marketing says we can only sell 40 M16 A1 Retro butt stocks.
Labor hours required for each product varies. It takes 5 hours of labor to make M16 A1 Retro butt stock, 4 hours for conventional butt stocks, 3 hours for the forward hand grip, 2 hours for the colt cobra, and 1 hour for the forward grip.
Machine time takes 3 hours for M16 A1 Retro butt stock, 1 hour for conventional butt stocks, 4 hours for the forward hand grip, 5 hours for colt cobra grip, and 2 hours to make forward grips.
Decision variable: X1 = Conventional Stocks
X2 = Hand grips
X3= Forward hand grip
X4= Colt Cobra grip
X5= M16 Retro butt Stock
LINEAR PROGRAMMING PROBLEM
MAX 3X1+4X2+6X3+8X4+10X5
S.T.
1) 4X1+1X2+3X3+2X4+5X5<60
2) 1X1+2X2+4X3+5X4+3X5<80
3) 50X2<50
4) 30X4>30
5) 40X5<40
OPTIMAL SOLUTION
Objective Function Value = 143.333
Variable Value Reduced Costs
————– ————— ——————
X1 6.667 0.000
X2 1.000 0.000
X3 0.000 0.944
X4 13.667 0.000
X5 1.000 0.000
Constraint Slack/Surplus Dual Prices
————– ————— ——————
1 0.000 0.389
2 0.000 1.444
3 0.000 0.014
4 380.000 0.000
5 0.000 0.093
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
———— ————— ————— —————
X1 1.600 3.000 6.526
X2 3.278 4.000 No Upper Limit
X3 No Lower Limit 6.000 6.944
X4 6.692 8.000 9.857
X5 6.278 10.000 No Upper Limit
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
———— ————— ————— —————
1 36.000 60.000 288.000
2 23.000 80.000 140.000
3 0.000 50.000 1678.571
4 No Lower Limit 30.000 410.000
5 0.000 40.000 292.632
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One page analysis of the output related to the problem. The following questions should be answered in the analysis. What is the objective function
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- Author David Lee
- Published December 8, 2021