A metropolitan area is facing waste management challenges. Its current landfill is almost full and it is looking for other sites that can fulfill its future needs. A landfill must not only be large enough to handle the weekly needs of the region, but must also adhere to environmental regulations. This means that the types of materials placed in the landfill must not exceed certain threshold limits. Metro officials are mainly concerned with satisfying the needs for disposal in the least costly manner possible. To simplify the problem of analyzing one particular site, the metropolitan planners have divided the region into three major areas and estimated the amount of waste (in tons) that can be transported from each part of the region (due to public opposition to the number of trucks on the local roads) per week. In addition, the amount of non-organic material per ton deposited in the landfill must be kept at a minimum to derive maximum capacity from the landfill over its useful life. The absolute limit of non-organic material per week in the landfill will be a composite 800 pounds per ton. For the landfill site under consideration, metro officials aim to identify amounts from the areas that will result in the least cost for the region. Useful data is shown in the following table. Area 1 Area 2 Area 3 Cost ($/ton) 100 110 125 600 900 Supply limit per 500 week Non-organic 900 825 600 (lbs/ton) er the following questions. (10 points) If planners are expecting the landfill to handle 1,200 tons per week, what is the optimal distribution of waste from the three areas in the region and what is the optimal cost? Formulate a linear program you can use to solve the problem. Solve the problem using Excel Solver and submit your linear program solution and sensitivity analysis sheet. Suppose you want to do a sensitivity analysis on your results. In particular, you want to find out the following: How would the optimal cost change if you were able to obtain 700 tons per week from area 2 instead of the current 600 tons? Should how you calculated this answer by referencing your sensitivity analysis form. Suppose a trucking firm extends an offer to the city officials to lower the cost of transporting waste from area 3 from $125/ton to $120/ton, what effect will this change have on the optimal values of the decision variables? On the optimal cost