The following network describes a transshipment scenario in which there are four sources A, B, C, and D, there are four destinations P, Q, and R, and S, and there are three intermediary distribution centers X, Y, and Z as shown. Each line segment indicates an existing shipping route, and the value next to each line segment represents the cost of shipping for one unit of an item from the source on the left of that line to the destination on the right of it. Furthermore, each of the three intermediary distribution facilities X, Y, and Z can handle only up to 50,000 units to be loaded/unloaded at that facility. The sources' supplies capacities and the destinations' demands are given in the following table.

Set up this transshipment problem R to determine the optimal number of units to be transported from each source to each destination. Use the LpsolverAPI in R to solve the problem. Highlight the optimal transportation cost in your report.