Problem $10-07($Algorithmic$)$

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 MWs$),$ and the cost to supply electricity to each market from each power generation plant $($prices are in $$/$MW$).$

Distribution Costs

City Los Angeles Tulsa Seattle Demand $($MWs$)$

Seattle $$332\mathrm{.}25$ $$569\mathrm{.}75$ $$35\mathrm{.}38926\mathrm{.}00$

Portland $$369\mathrm{.}25$ $$606\mathrm{.}75$ $$191\mathrm{.}13844\mathrm{.}25$

San Francisco $$173\mathrm{.}13$ $$470\mathrm{.}00$ $$291\mathrm{.}882370\mathrm{.}00$

Boise $$333\mathrm{.}25$ $$452\mathrm{.}00$ $$273\mathrm{.}88570\mathrm{.}75$

Reno $$242\mathrm{.}50$ $$480\mathrm{.}00$ $$361\mathrm{.}25955\mathrm{.}00$

Bozeman $$411\mathrm{.}63$ $$411\mathrm{.}63$ $$292\mathrm{.}88589\mathrm{.}75$

Laramie $$395\mathrm{.}25$ $$454\mathrm{.}63$ $$395\mathrm{.}251226\mathrm{.}50$

Park City $$391\mathrm{.}25$ $$391\mathrm{.}25$ $$510\mathrm{.}00747\mathrm{.}50$

Flagstaff $$199\mathrm{.}13$ $$496\mathrm{.}00$ $$614\mathrm{.}751208\mathrm{.}50$

Durango $$332\mathrm{.}25$ $$272\mathrm{.}88$ $$569\mathrm{.}751519\mathrm{.}75$

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? If required, round your answers to two decimal places.

The optimal solution is to produce fill in the blank $1$

MWs in Los Angeles, fill in the blank $2$

MWs in Tulsa, and fill in the blank $3$

MWs in Seattle. The total distribution cost of this solution is $ fill in the blank $4$

$.$

If at most $4100$ MWs 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? If required, round your answers to two decimal places.

The optimal solution is to produce fill in the blank $5$

MWs in Los Angeles, fill in the blank $6$

MWs in Tulsa, and fill in the blank $7$

MWs in Seattle. The total distribution cost of this solution is $ fill in the blank $8$

$.$ The increase in cost associated with the additional constraints is $ fill in the blank $9$

$.$