One page analysis of the output related to the problem. The following questions should be answered in the analysis. What is the objective function

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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