Problem $3(10$ Points$)(-2/$error$)$

XYZ Manufacturing Company operates five plants in Appleton, WI$,$ Oshkosh, WI$,$ Omaha, NE$,$ Terre Haute, IN$,$ & Toledo, OH$.$ The company ships products from it plants to its distribution centers $($DCs$)$: DC $1,$ DC $2,$ & DC $3.$ You are given the data below regarding plant capacities, annual fixed costs for the plants $($incurred if and only if the plant is used and ships greater than $0$ units$),$ manufacturing cost per unit $+$ shipping cost per unit, and demand at each DC$.$

Note: The CEO has mandated that the Terre Haute plant MUST be used. You will need to add a constraint for this mandate and to show your additional work.

Formulate a model to determine which plants to use to minimize total cost.