Please solve the problem using Excel Solver.

DGD is a midstream energy company. They are considering 2 offers for some of their product (consider this the revenue earned in the distribution of product).

Offer #1 - 125 barrels at $55/barrel. Pick up at location ALPHA.

Offer #2 - 115 barrels at $45/barrel. Pick up at location BETA.

Product is located at two storage areas.

Storage Area 1 - 120 barrels, each barrel costs $13.

Storage Area 2 - 90 barrels, each barrel costs $15.

There is a leased distribution network used by DGD to send product from where it is located (SA1, SA2) to where it is sold to their customer (ALPHA, BETA). There are 5 intermediate nodes (A,B,C,D,E). Each link in the distribution network has a capacity and a per barrel cost. See the graphic.

Setup a Goal Programming model that determines how to optimally ship product through the distribution network. Based on the following goals in priority order. Assume all sub goals are equal.

System constraints: Demand cannot be exceeded, supply cannot be exceeded, link capacity cannot be exceeded, and barrels of product cannot magically appear and disappear.

Goal 1: Try to send at least 80% of the product located at each storage area (individually).

Goal 2: Try to distribute product such that at least 70% of the offer requests for product are met - this would be at ALPHA and at BETA.

Goal 3: Try to achieve at least $2900 in profit (revenue less the storage costs of product used less the distribution cost).

Goal 4: Try to keep distribution costs less than $2750 (just distribution costs alone).

Goal 5: With the exception of the D-E, E-D, D-ALPHA and E-BETA links, try to limit flow across any link to no more than 35 barrels.

Do not worry about integers. Summarize which goals were achieved and which ones were not.

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