A factory requires at least 4 Mgal/day more water than it is currently using. A water supply facility can supply up to 10 Mgal/day of additional water with a BOD of 50mg/L, and a local stream can supply an additional 2 Mgal/day with a BOD of 200 mg/L. After use, the factory discharges the water is used to a local river. The concentration of biochemical oxygen demand (BOD) in the wastewater released to a nearby river must be less than 100mg/L. The cost of water is $1000/Mgal from the water supply facility and $150/Mgal from the local stream. The factory has obtained financing that allows them to spend no more than $3500/day on water.
a. Formulate a systems model and find the minimum cost solution that satisfies all constraints.
b. Then, reformulate the model for minimum discharge BOD solution that satisfies all constraints.
c. Plot the two solutions to the previous problem on a graph that has cost on the horizontal axis and BOD on the vertical axis. Draw a line connecting these two different optima and determine the slope of that line.
d. Propose a new environmental policy that would cause a profit-maximizing factory manager to put in place the BOD-minimizing design.