A steel company must decide how to allocate next week’s time on a rolling mill, which is a machine that takes unfinished slabs of steep as input and can produce either of two semi-finished products: bands and coils. The mill’s two products come off the rolling line at different rates:
Bands 200 tons/hour
Coils 140 tons/hour
They also produce different profits:
Bands $25/ton
Coils $30/ton
Based on currently booked orders, the following upper bounds are placed on the amount of each product to produce:
Bands 6,000 tons
Coils 4,000 tons
Given there are 40 hours of production time available this week, determine how many tons of bands and coils that should be produced to yield the greatest profit.