Formulations done in class Set 2.pdf - Formulations for Common Business Applications of LP(Class 4 1 Decision Variables Ci acres of plot i planted with

Formulations done in class Set 2.pdf - Formulations for...

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Formulations for Common Business Applications of LP (Class 4) 1. Decision Variables Ci acres of plot i planted with corn (i=1,2,3) Pi acres of plot i planted with peas (i=1,2,3) Si acres of plot i planted with soy bean (i=1,2,3) Objective Function Maximize z = 600[C1 + C2 + C3] + 450[P1 + P2 + P3] + 300[S1 + S2 + S3] Constraints Available land plot 1: C1 + P1 + S1 < 500 Available land plot 2: C2 + P2 + S2 < 800 Available land plot 3: C3 + P3 + S3 < 700 Max corn: C1 + C2 + C3 < 900 Max peas: P1 + P2 + P3 < 700 Max soya: S1 + S2 + S3 < 1000 At least 60% of plot 1 cultivated: C1 + P1 + S1 > 300 At least 60% of plot 2 cultivated: C2 + P2 + S2 > 480 At least 60% of plot 3 cultivated: C3 + P3 + S3 > 420 Proportion of plot 1 and 2 in cultivation: 800C1 + 800P1 + 800S1 - 500C2 - 500P2 - 500S2 = 0 Proportion of plot 2 and 3 in cultivation: 700C2 +700P2 + 700S2 - 800C3 - 800 P3 - 800 S3 = 0 2. Decision Variables Bf: # of lbs of beef in fore Ba: # of lbs of beef in aft Gf: # of lbs of grain in fore Ga: # of lbs of grain in aft Objective Function Maximize z= 0.35 (Bf + Ba) + 0.12(Gf + Ga) Constraints Fore cargo weight capacity: Bf + Gf < 70,000 Aft cargo weight capacity: Ba + Ga < 90,000
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