The household sector is the largest consumer of energy in India,6 requiring at least 108 kilowatthours per day in a large city such as Madras.

This energy can be obtained from sources j = 1 kerosene, j = 2 biogas, j = 3 photovoltaic, j = 4 fuelwood-generated electricity, j = 5 biogas-generated electricity, j = 6 diesel-generated electricity, and j = 7 electricity from the national power grid, with efficiencies hj expressing the number of kilowatthours per unit of original fuel input of source j. Biogas is limited 1.3 * 109 units. Energy planners are looking for the best mix of these sources to meet the 108 requirement in terms of a variety of conflicting objectives. One is low total cost at pj per unit source j. Another is to maximize local employment, which is estimated to grow at ej per unit of energy source j. Finally, there are three types of pollution to be minimized: carbon oxides produces at cj per unit of source j, sulfides at sj per unit of j, and nitrogen oxides at nj per unit of j.

(a) Formulate a multiobjective LP to choose a best mix of sources.

(b) Revise your model as a goal program with maximum targets P, C, S, and N for cost, carbon, sulfur, and nitrogen, together with minimum target E for employment.