Sunco Oil produces oil at two wells. Well 1 can produce as many as 350,000 barre

Question

Sunco Oil produces oil at two wells. Well 1 can produce as many as 350,000 barrels per day, and well 2 can produce as many as 200,000 barrels per day. Assume that before being shipped to Los Angeles or New York, all oil produced at the wells must be refined at either Galveston or Mobile. To refine 1,000 barrels of oil costs $27 at Mobile and $15 at Galveston. Los Angeles requires 200,000 barrels per day, and New York requires 260,000 barrels per day. The costs of shipping 1,000 barrels between two points are shown in the table at the right. Assuming that both Mobile and Galveston have refinery capacity of 235,000 barrels per day each.

a.      Formulate a linear programming model to minimize the daily cost of transporting and refining the oil requirements of Los Angeles and New York.

Clearly define the decision variables

Define the objective function:

      Define the constraints

Explanation / Answer

Decision variables:

W1: no. of barrels in 1000 produced from well1

W2: no. of barrels in 1000 produced from well2

M: no. of barrels in 1000 REFINED IN Mobile refinery

G: no. of barrels in 1000 REFINED IN Galveston refinery

L: no. of barrels in 1000 transported to Loss Angeles

N: no. of barrels in 1000 transported to NEW Yark

Objective function:

Minimize total cost Z= 27M + 15G + C1*L + C2*N

(Where C1 & C2 are the costs of shipping 1,000 barrels between two points which is not given here)

Constraints:

Supply:

W1<=350; W2<=200

Demand:

L>=200; N>=260

Logical constraints:

W1+W2=M+G = L+N

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