A copper manufacturer receives 10,000 tons of chalcopyrite (CuFeS2) a month

Subject:MathPrice:9.82 Bought3

Share With

A copper manufacturer receives 10,000 tons of chalcopyrite (CuFeS2) a month. Chalcopyrite is first refined, producing blister copper. Blister copper is then purified. Depending on the purification process, the manufacturer can produce three grades of copper: Cu-A, Cu-B and Cu-C. Manufacturing process specifications are given below.

process refinement purification-A purification-B purification-C

output
1 ton of blister copper 1 ton of Cu-A
1 ton of Cu-B
1 ton of Cu-C

requirements

10 tons of chalcopyrite 2 tons of blister copper 3 tons of blister copper 5 tons of blister copper

20 machine-hours 30 machine-hours 50 machine-hours 60 machine-hours

So, for example, in order to produce 1 ton of Cu-A, you need 2 tons of blister copper and 30 machine- hours.

Market prices for Cu-A, Cu-B and Cu-C are $350, $500, $700 per ton. The manufacturer can also sell blister copper for $150 per ton. There are 50,000 machine-hours available each month. Formulate a profit maximization LP to determine copper production plan.

Hint: introduce separate variables for the amounts of blister copper produced and sold. Then make sure you keep track of machine-hours and chalcopyrite availability.