MEK Products has two factories located in Minneapolis and Detroit with weekly production capacities of $300$ and $250$ units, respectively. Four customer centers in the cities of Cleveland, Dayton, Louisville, and Peoria have weekly product requirements of $100,130,140,$ and $160$ units, respectively. Unit shipping costs for each factory$-$customer center pair are shown in the table below, along with the other data for the problem. MEK seeks minimizes the total weekly shipping cost while satisfying all factory capacity and customer requirements.

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Which of the follow are true at the optimal solution?

Group of answer choices

A $5-$unit increase in the demand at Dayton will increase the total shipping cost by $$200.$

A $10-$unit increase in the demand at Peoria will decrease the total shipping cost by $$300.$

A $20-$unit increase in the demand at Louisville will increase the total cost by $$1060.$

A $100-$unit increase in the supply at Detroit will decrease the total cost by $$800.$

Exactly two answers are correct.

None of the answers are correct.