Consider the oil pipeline network shown below. Different nodes represent pumping, receiving, and transshipment stations. Distances in miles between the stations are shown on the network. The supply of Node $1$ is $50,000$ gallons of oil. The supply of Node $3$ is $60,000$ gallons of oil. The demands of Nodes $2$ and $4$ are $90,000$ and $20,000$ gallons, respectively. The managers want to determine the optimal shipping routes to meet the demand.

a$)$ Define the variables.

b$)$ Formulate the problem as a transshipment model.

c$)$ Solve the problem in Excel Solver and submit your file in Canvas.

d$)$ State the optimal solution of the problem here.