WSCC, Texas's main provider of electrical energy, has three primary power plants, one in Charleston, one in Bartown and the other in York. For planning purposes, WSCC divides the state of Texas into four geographic areas: East, North, South and the West. Given below are the transmission costs when providing energy from each power plant to each region (per GWh). Power Plant York Charleston Bartown Power Plant York East Charleston Bartown $0.50 $2.25 $2.10 East North 0.01 0.07 0.04 $1.20 $2.00 $1.25 It is known that some energy is lost when it is transmitted (through transformers and power lines) from source to destination. The matrix below provides the estimated loss in energy when transmitted from power-plant to region (e.g., there is a 2% loss when supplying energy from Charleston to South) North South 0.03 0.02 0.02 $1.35 $1.50 $1.00 South West 0.03 0.02 0.03 $2.00 $0.50 $0.10 West 0.06 0.01 0.02 The power generation capacities for York, Charleston and Bartown are 1.10 GWh, 1.80GWh and 1.20 GWh respectively. Likewise, the demand for the East, Baryburg, Suburban DC and the West are 0.73 GWh, 1.30 GWh, 1.25 GWh, and 0.64 GWh respectively. a. What is the least cost energy plan that FSE should follow? b. WSCC has received approval to add 100 MWh (0.1 GWh) to one of its power plants. Using sensitivity analysis, determine which power plant should receive the upgrade. What impact will that have. if any. on the overall cost? fusing sensitivity analysis only1