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?

If the cost of shipping from the Jersey City DC to the Minneapolis warehouse increases by $$4$ per unit, then only the solution value will change.

If the cost of shipping from the Riverside DC to the Atlanta warehouse decreases by $$5$ per unit, then the optimal solution will change.

Exactly two answers are correct.

If the cost of shipping from the Jersey City DC to the Minneapolis warehouse decreases by $$5$ per unit, then the optimal solution will not change.

If the cost of shipping from the Riverside DC to the Atlanta warehouse increases to $$50$ per unit, then both the optimal solution and the solution value will change.