Question Content Area

Problem $6-07$

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

Distribution costs

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

Seattle $356\mathrm{.}25593\mathrm{.}7559\mathrm{.}38950\mathrm{.}00$

Portland $356\mathrm{.}25593\mathrm{.}75178\mathrm{.}13831\mathrm{.}25$

San Francisco $178\mathrm{.}13475\mathrm{.}00296\mathrm{.}882375\mathrm{.}00$

Boise $356\mathrm{.}25475\mathrm{.}00296\mathrm{.}88593\mathrm{.}75$

Reno $237\mathrm{.}50475\mathrm{.}00356\mathrm{.}25950\mathrm{.}00$

Bozeman $415\mathrm{.}63415\mathrm{.}63296\mathrm{.}88593\mathrm{.}75$

Laramie $356\mathrm{.}25415\mathrm{.}63356\mathrm{.}251187\mathrm{.}50$

Park City $356\mathrm{.}25356\mathrm{.}25475\mathrm{.}00712\mathrm{.}50$

Flagstaff $178\mathrm{.}13475\mathrm{.}00593\mathrm{.}751187\mathrm{.}50$

Durango $356\mathrm{.}25296\mathrm{.}88593\mathrm{.}751543\mathrm{.}75$

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?

Los Angeles, Tulsa, Seattle

should be supplied by which power plants.

Round your answers to $2$ decimal places.

fill in the blank $2$

$6,412\mathrm{.}5$

MWs in Los Angeles

fill in the blank $3$

$1,543\mathrm{.}75$

MWs in Tulsa

fill in the blank $4$

$2,968\mathrm{.}75$

MWs in Seattle

What is the total annual power distribution cost for this solution?

Round your answer to the nearest cent.

The total distribution cost is $ fill in the blank $?$

If at most $4000$ MW of power can be supplied by any one of the power plants, what is the optimal solution?

Round your answers to $2$ decimal places.

fill in the blank $6$

$4,000$

MWs in Los Angeles

fill in the blank $7$

$2,925$

MWs in Tulsa

fill in the blank $8$

$4,000$

MWs in Seattle

Round your answer to the nearest cent.

The total distribution cost is $ fill in the blank $?$

What is the annual increase in power distribution cost that results from adding these constraints to the original formulation?

Round your answer to the nearest cent.

The increase in cost is $ fill in the blank $10$

$100,569\mathrm{.}750$