1.14 Production Planning of a Wires Manufacturer A firm in Valencia manufactures aluminium and copper wires. Each kg of alu- minium wire requires 5 kWh of electricity and 0.25 h of labour. Each kg of copper wire requires 2 kWh of electricity and 0.5 h of labour. Copper wire production would be restricted by the fact that the quantity of raw materials available permits the maximum production of 60 kg/day. Electricity is limited to 500 kWh/day and labour to 40 h/day. The aluminium wire profit is $0.25/kg, while the copper wire profit is $0.4/kg. What quantity of each wire should be produced to maximise the profit and what would the profit be? Solution Decision variables: X= kg manufactured of aluminium wire Y = kg manufactured of copper wire Objective function: To maximise z= 0.25X + 0.40Y Constraints: Y 0 Y 20 As it is a problem with two decision variables, it can be solved graphically to obtain the solution below: x= 85 Y= 37.5 Z= 36.25