AgCorp produces two types of fertilizer for sale to midwestern farmers by blending together five raw materials. Each raw material contains some level of six nutrients. The two types of fertizer sold by AgCorp have maximum and minimum levels specified for each of the six nutrients. The goal of this problem is to inform AgCorp executives of the optimal mix of the five materials for each of its two types of fertilizer with the goal of minimizing the total cost of product for the two products. The amount of the nutrients contained in each of the five raw materials are shown in the table below. The entries in the table are the proportion, by weight, of each nutrient found in the indicated raw material. (N is nitrogen, P is phosphorous, K is potassium and Mo is molybdenum.) Material Sewage 1 Sewage 2 Manure Industrial Waste Compost Micronutrients Zinc Colbalt Mo Cost ($/lb.) 0.001 0.002 0.001 0.007 0.001 0.25 0.15 0.006 0.005 0.004 0.20 0.20 0.20 0.001 0.001 0.001 Proportion, by Weight Major P N K 0.30 0.05 0.03 0.35 0.07 0.02 0.30 0.10 0.05 - Fertilizer Type A min max Type B min max 0.003 0.004 0.002 For each type of fertilizer AgCorp has specified a minimum and maximum proportion for each of the six nutrients. These limits are shown below: Max/Min Proportion, by Weight N | P | K Zinc Colbalt Mo 0.100 0.060 0.100 0.003 0.002 0.002 0.300 0.180 0.140 0.005 0.003 0.003 0.45 0.48 0.57 0.250 0.080 0.080 0.002 0.001 0.004 0.330 0.220 0.120 0.004 0.004 0.005 0.26 0.39 Type A fertilizer sells for $0.34 per pound and Type B fertilizer sells for $0.44 per pound. Lastly, AgCorp wants to produce between 50,000 and 70,000 pounds of Type A fertilizer and between 100,000 and 135,000 pounds of Type B fertilizer. It can sell all that it produces. What is the maximum profit (revenue minus costs) AgCorp can make from this part of its operations? How much of each fertizer should be produced? How much of each raw material should be purchased, and what fraction, by weight, of each fertizer type is made up of each raw material? Be sure to show the linear program that leads to your conclusions, including a clear definition of all decision variables and structural constraints. You may use technology to solve your linear program.