The port of Lajitas has three loading docks. The distance (in meters) among the loading docks is given in the following table:

Three tankers currently at sea are coming into Lajitas. It is necessary to assign a dock for each tanker. Also, only one tanker can anchor in a given dock. Currently, ships 2 and 3 are empty and have no cargo. However, ship 1 has cargo that must be loaded onto the other two ships. The number of tons that must be transferred is as follows:

Formulate and solve with Excel Solver or LINGO an optimization problem that will assign ships to docks so that the product of tonnage moved times distance is minimized. (Hints: This problem is an extension of the assignment problem introduced in Chapter 10. Also, be careful with the objective function. Only include the nonzero terms. Each of the 12 nonzero terms in the objective function is a quadratic term, or the product of two variables.) There are 12 nonzero terms in the objective function.