An (extremely simplified) STEEL COMPANY must decide how to allocate next week's time on a rolling mill. The mill takes unfinished slabs of steel as input, and can produce either of two semi-finished products, which we will call bands and coils. The mill's two products come off the rolling line at different rates: Tons per hour: Band 200 Coils 140 and they also have different profitabilities: Profit per ton: Band Coils $25 $30 To further complicate matters, the following weekly production amounts are the most that can be justified in light of the currently booked orders: Maximum tons: 6000 4000 Band Coils If 40 hours of production time are available this week, the question facing the company is as follows: how many tons of bands and how many tons of coils should be produced to maximize the total profit? Formulate a linear programming model to represent the problem then solve it.