A small town requires the daily consumption of 6 million gallons of water of a quality such that the concentration of salt must be kept below 100 mg/gal and the concentration of iodine be kept below 12 mg/gallon. The water can be supplied from three sources: from local wells, from a local river, or from an out-of-state river. In each case, the cost of the necessary infrastructure (pipes, pumps, long term repairs and replacements, those sort of things) will be financed by floating bonds, which will be repaid by the users in their water bill.
Water from the local wells will have 50 mg/gal of salt, and 10 mg/gal of iodine, and can be supplied at a cost of $150/million gallons. Water from the local river will have 150 mg/gal of salt, and 2 mg/gal of iodine, and can be supplied at a cost of $75/million gallons. Water from the out-of-state river will have 20 mg/gal of salt, and no iodine, and can be supplied at a cost of $250/million gallons.
The water from the three sources will be completely mixed before it is used. Draw a scale map (schematic) of this problem, then draw a model (circles, arrows, neatly lined up), and then write a mathematical model to solve for the least expensive way to supply the water, and finally, solve the problem using MOR/LP.
NOTE: On all linear programming problems in this class:
- Formulate the written solution necessary to be typed into into MOR. For example:
Max Z = 3x+2y
- COMPLETELY define at least one or two of the variables so that I will know what you are doing. For example: AB = the number of cubic yards of dirt that I find it to be in my best economic interest to haul from the borrow pit at A to the fill station at B.
- Solve the problem using MOR.
- COMPLETELY define your solution. Do not just hand in the computer output and expect that I can interpret it. That gets you only half credit. Rather, tell me exactly what the output means: For example if AB = 12, tell me that you have found you should haul 12 tons of gravel from Pit A to Job Site 2. JBO = 3 means you should make three base plates in January using overtime. Whatever.
If you do not follow these instructions, you will get zero credit for your work.