ABC Trucking has three distribution centers $($DCs$)$ located in Dallas, Jersey City, and Riverside that transport product each week to warehouses located in five cities: Seattle, Topeka, Minneapolis, Atlanta, and Boston. Each DC has an upper limit on the number of units of product that it can ship each week and each warehouse has a requirement for the volume of product needed. These values and the per unit shipping costs for all DC$-$warehouse pairs are provided in the accompanying Excel workbook.

ABC seeks a feasible shipping plan that minimizes the total shipping cost.

Let $x_{\text{I}}K$ be the amount shipped from DC$,$ for I $=$ D$,$ J$,$ R$,$ to the warehouse $K,$ for $K=S,T,M,$ A$,$ B$.$ Note the letters correspond to the first letter of the cities above. For example, X$\_$DS is the amount shipped from Dallas to Seattle.

Which of the following statements are true for the ABC shipping problem?

None of the answers are correct.

We would never ship from Jersey City to Minneapolis as it is too expensive.

The optimal solution to the ABC problem could include X$\_$JA $=70.$

A feasible solution to the ABC problem could include X$\_$DM $=110.$

There are feasible solutions where all constraints are binding $($zero$-$slack$).$