Power Distribution. 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$$s major residential markets, the annual demand in each market $($in megawatts or MW$),$ and the cost to supply electricity to each market from each power generation plant $($in $$/$MW$).$ LO $1$

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Distribution Costs $($$$/$MW$)$

City

Los Angeles

Tulsa

Seattle

Demand $($MW$)$

Seattle

$356\mathrm{.}25$

$593\mathrm{.}75$

$59\mathrm{.}38$

$950\mathrm{.}00$

Portland

$356\mathrm{.}25$

$593\mathrm{.}75$

$178\mathrm{.}13$

$831\mathrm{.}25$

San Francisco

$178\mathrm{.}13$

$475\mathrm{.}00$

$296\mathrm{.}88$

$2375\mathrm{.}00$

Boise

$356\mathrm{.}25$

$475\mathrm{.}00$

$296\mathrm{.}88$

$593\mathrm{.}75$

Reno

$237\mathrm{.}50$

$475\mathrm{.}00$

$356\mathrm{.}25$

$950\mathrm{.}00$

Bozeman

$415\mathrm{.}63$

$415\mathrm{.}63$

$296\mathrm{.}88$

$593\mathrm{.}75$

Laramie

$356\mathrm{.}25$

$415\mathrm{.}63$

$356\mathrm{.}25$

$1187\mathrm{.}50$

Park City

$356\mathrm{.}25$

$356\mathrm{.}25$

$475\mathrm{.}00$

$712\mathrm{.}50$

Flagstaff

$178\mathrm{.}13$

$475\mathrm{.}00$

$593\mathrm{.}75$

$1187\mathrm{.}50$

Durango

$356\mathrm{.}25$

$296\mathrm{.}88$

$593\mathrm{.}75$

$1543\mathrm{.}75$

$1)$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?

I$2)$f at most $4000$ MW of power can be supplied by any one of the power plants, what is the optimal solution, and what is the annual increase in power distribution cost that results from adding these constraints to the original formulation?