Question

Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table shows Aggie Power Generation's major residential markets, the annual demand in each market (in megawatts or MW), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW). City Seattle Portland San Francisco Boise Reno Bozeman Laramie Park City Flagstaff Durango Los Angeles $356.25 $356.25 $178.13 $356.25 $237.50 $415.63 $356.25 $356.25 $178.13 $356.25 Distribution Costs Tulsa Seattle Demand (MW) $593.75 $59.38 950.00 $593.75 $178.13 831.25 $475.00 $296.88 2375.00 $475.00 $296.88 593.75 $475.00 $356.25 950.00 $415.63 $296.88 593.75 $415.63 $356.25 1187.50 $356.25 $475.00 712.50 $475.00 $593.75 1187.50 $296.88 $593.75 1543.75 a. If there are no restrictions on the amount of power that can be supplied by any of the power plants, what is the optimal solution to this problem? Which cities should be supplied by which power plants? What is the total annual power distribution cost for this solution? b. If at most 4000 MW of power can be supplied by any one of the power plants, what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation?

Answer 1

Page Not. ) Answed hu Cliven data Distribution corts Cindy los Angeles, Tulso seattle Demand Seattle, 7356 35 +593 75 759 38 950.00 Portland 2356 25 1593.75 7178.13 831.25 soun Bouncixo &178 B 5475 0029688 2375.00 Boire 2356 25 2475.00 2296.88 593.00 Reno 2237.50 5475.00 7356.25 Bozeman 7415 63 415. 63 2296.88 593.75 Maramie 35695 2415 63 2356 95 1187 5o Park City 2356.25 2356 25 475.00 712.50 lagsball (£178.13 €475.60 5993.75 Durango 2356-25 2296.88 2893.75 1543.75 Meattle, (a). Minimum distribution host table Distribution Cort City lost Angeles Tulsa seattle Demand 559.38 950. pootland 7 178 13 831.25 San Francisco 7 178.13 3375 boise 7296.88 593.75 - Reno 2237 50 950 Bozeman 129688 593.75 Parmic 2356 25 11187.5 park city 7 356.95 712.5 Flagstaff 7178.13 1187.5 Dodango [5296.88

Page No. 2 Power production table for plant & Distribution cost City los Angeles Tulsa seattle Demand 1 950 950 Portland 83185 831.25 Sun Brancisco 2375 2375 ibose 1593.75 593.75 | Reno 950 Bozeman 1593.75 593:25 Claramie 1187:5 118715 Ipark city 712.5 712.5 trlogstobo 1187.5 1187.8 Durango 1543.75 1543 TS 16412.5 / 1543.75 2968.751 950 > The optimal solution is to produce 5412.5mws in Los Angles 11543 75mws in Tulsa 2968:75 MWS in Seattle

Page No 3 -b optimal selisticon * Power Po'etribution.com City lost Angles Tulsa seattle Demant seattle 950 - 950 Sportland 831.25 831.25 San Fancisco 2375 2375 I bose 593.75 593.75 Reno 950 950 Boleman 593.75 593.75 Hloramic 156.25 1031.95 | 1187.5 park city 712.5 27125 Klagstaff 518.75 | 668.75 1187.5 Duxango 1543.75 1543.75 Lotal 4000 I 2925 | Hooo 1 10985 to produce The optimal solution is 4000 mws in los Angeles 2925mws in Tulsa 4000 MWs in Seattle.

Page No - 4 Total Distribution cost bothies holistienis 32,150,159 Distribution cost - city lost Angeles Tulsa reattle Demand seattle 56411 950 potland 148070.5625 83/25 San Pancisco 423058.75 2375 boise 1762225 593.75 | Reno 225629 950 & Bozeman 176272 5 593.75 Ilarame 556646625 367387835 1187.5 Ipark city 712.5 Flagstaff 192404.9375 317656 • 25 1187.5 Durango 4583085 1543. 75 796752 75 1029792.875 924409.375 275095s