Read the problem. Describe the bounds, limitations, requirements, proportional r
ID: 3292492 • Letter: R
Question
Read the problem. Describe the bounds, limitations, requirements, proportional relationships, or balance constraints that are in the problem.
The Martinez Model Car Company produces four different radio-controlled model cars based on exotic production models: Ferrari, BMW, Lotus, and Tesla. Each model requires production in five departments: molding, sanding, polishing, painting, and finishing. The number of minutes required for each product in each department, the selling price per unit, and the minutes available in each department each day are shown below. FerrariBMW Lotus Tesla Minutes Available Molding 5.00 3.50 1.00 3.00 600 Sanding 4.00 3.20 2.00 3.65 600 |Polishing|350 200 300 100 480 | 1 1175 1200 1480 Polishing3.50 2.00 3.00 1.00 480 Painting 3.75 3.25 1.752.00 480 Finishing 4.00 1.00 2.00 3.00 480 Price$350.00 $330.00 $270.00 $255.00Explanation / Answer
Objective function is depends on decision variables, which are X1, X2, X3 and X4 for Ferrari, BMW, Lotus and Tesla respectively.
Thus, Objective function is
Zmax = 350X1 +330X2 +270X3 +255X4
Molding constraints
5X1 +3.5X2 +X3 +3X4 <= 600
Sanding constraints
4X1 +3.2X2 +2X3 +3.65X4 <= 600
Polishing constraints
3.5X1 +2X2 +3X3 +X4 <= 480
Painting constraints
3.75X1 +3.25X2 +1.75X3 +2X4 <= 480
Finishing constraints
4X1 +X2 +2X3 +3X4 <= 480
Non-negative constraints
X1 >=0, X2 >=0, X3 >=0, X4 >=0
Hence, model is
Zmax = 350X1 +330X2 +270X3 +255X4
5X1 +3.5X2 +X3 +3X4 <= 600
4X1 +3.2X2 +2X3 +3.65X4 <= 600
3.5X1 +2X2 +3X3 +X4 <= 480
3.75X1 +3.25X2 +1.75X3 +2X4 <= 480
4X1 +X2 +2X3 +3X4 <= 480
X1 >=0, X2 >=0, X3 >=0, X4 >=0
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