Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors
The current inventory levels and parts list for each type of fan is shown in the table.
Fan A Fan B Fan C
Component # Needed # Needed # Needed Current Inventory
Wire 1 2 3 500
Nuts 8 12 14 700
Bolts 8 12 14 700
Motor 1 1 2 200
Blades 5 6 7 400
Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.
Let A = units of Fan A
B = units of Fan B
C = units of Fan C
Max Z = 18A + 25B + 30C
s.t. 1A + 2B + 3C = 500 Wire constraint
8A + 12B + 14C = 700 Nuts constraint
8A + 12B + 14C = 700 Bolt constraint
1A + 1B + 2C = 200 Motor constraint
5A + 6B + 7C = 400 Blades constraint
A, B, C > 0
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