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.

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

$$The Dallas Distribution Center $($DC$)$ constraint has non$-$zero slack.

$$Exactly two answers are correct.

$$The Jersey City$-$Minneapolis shipping lane has positive product flow.

$$The Topeka Warehouse constraint has non$-$zero slack.

$$The Dallas$-$Boston shipping lane has positive product flow.