Question

1. 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	$364.25	$601.75	$67.38	958.00
   Portland	$367.25	$604.75	$189.13	842.25
   San Francisco	$166.13	$463.00	$284.88	2363.00
   Boise	$341.25	$460.00	$281.88	578.75
   Reno	$241.50	$479.00	$360.25	954.00
   Bozeman	$428.63	$428.63	$309.88	506.15
   Laramie	$367.25	$426.63	$367.25	1198.50
   Park City	$375.25	$375.25	$494.00	622.25
   Flagstaff	$238.13	$535.00	$653.75	1178.19
   Durango	$363.25	$303.88	$600.75	1472.25

   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? 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  MWs in Los Angeles,  MWs in Tulsa, and  MWs in Seattle. The total distribution cost of this solution is $  .
      
   2. If at most 4000 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  MWs in Los Angeles,  MWs in Tulsa, and  MWs in Seattle. The total distribution cost of this solution is $  . The increase in cost associated with the additional constraints is $  .

Answer 1

a. Following is the screenshot of the Excel Sheet used to solve this problem with the Formulas also being shown for each cell.

These are the solver parameters used-

Here is the final solution of the sheet -

No surprise, all power is supplied by power plant closest to the city.

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Let us now add the constraint which limits the power being supplied.

Here is the solver config -

Here is the final solution -

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The New Cost is $2661568.24

The Old Cost was $2568386.69

Therefore, increase in cost is $93181.55