Toxic chemicals banned decades ago continue to linger in the River, threatening people and the environment. To
To address this situation, the state is going to build some pollution control stations. Three sites (Leavenworth, Cashmere, and Wenatchee) are under consideration. The state is primarily interested in controlling the pollution levels of two types of PCB pollutants (labeled PCB-A and PCB-B). The state legislature requires that at least 36,000 pounds of PCB-A and at least 54,000 pounds of PCB-B be removed from the river. The relevant data for this problem are shown below. If a station is built at a site (at the cost indicated below), it can treat an effectively unlimited amount of water, subject to the cost per ton of water treated as listed below. The last two rows indicate the number of pounds of each pollutant that is removed per ton of water treated. For example, if they treat two tons of water at Leavenworth, both 60 pounds of PCB-A and 48 pounds of PCB-B would be removed from the river.
The state would only consider building a station near Wenatchee if there is also a station built near Cashmere. Furthermore, the state can build on at most two of the three sites.
Build a linear programming spreadsheet model (with integer and/or binary variables if needed) that would determine where to build treatment stations and how many tons of water to treat at each station so as to meet the state legislature's requirements at the lowest possible total cost.