A metropolitan area is facing a serious problem with disposingof its waste. Its current landfill is almost full and it is lookingfor other sites that can fulfill its likely future needs. Alandfill must not only be large enough to handle the weekly needsof the region, but has to be as environmentally benign as possible.This means that the types of materials that are placed in thelandfill must not exceed certain threshold limits. And of course,officials are mainly concerned with satisfying the needs fordisposal in the least costly manner possible. To simplify theproblem of analyzing one particular site, the metropolitan plannershave divided the region into three major parts and estimated theamount of waste (in tons) that can be transported from each part ofthe region (due to public opposition to the number of trucks on thelocal roads) per week. In addition, the amount of nonorganicmaterial per ton deposited in the landfill must be kept at aminimum in order for the landfill to provide the maximum capacityover its useful life. It is expected that the absolute limit ofnon-organic material allowed per week in the landfill will be acomposite 900 pounds per ton. The relevant data is shown in thefollowing table.
| Location 1 | Location 2 | Location 3 |
| Cost ($/ton) | 120 | 115 | 105 |
| Supply limit per week | 490 | 635 | 900 |
| Non-organic (lb/ton) | 1250 | 800 | 550 |
a) Write out the set of linear equations needed for the problemassuming that planners expect the landfill to handle 1,850 tons perweek. That is, what equation do you want to optimize and whatequations would you use as constraints?
b) If planners are expecting the landfill to handle 1,850 tonsper week, what is the optimal distribution of waste delivery fromthe three locations in the region? (Hand in the results from Excel:linear program input sheet, the Answer Report, Sensitivity Report,and Limits Report) How much will the city pay per week for thelandfill service?
c) Suppose you want to do a sensitivity analysis on youranalysis. In particular, you are interested in answering thefollowing questions. How would the optimal cost change if you wereable to obtain 500 tons per week from location 3 instead of thecurrent 850 tons? Show how you would calculate this answer byreferencing your sensitivity analysis form.
d) Suppose a trucking firm comes to you and says that they couldlower the cost per ton of transporting waste from location 3 from$105 per ton to $95 per ton for a nominal fee (they're anxious toget the business). Using your results and sensitivity analysis frompart b, what effect will this change have on (i) the optimal cost?(ii) If the firm will charge the equivalent of a weekly flat fee of$1,000, should metro officials accept this offer?
