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

GoBigRed 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 Omaha 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.

Manufacturing Cost$/$ Unit $+$

Shipping Cost$/$Unit to DC

Plant

Annual

Fixed Cost DC $1$ DC $2$ DC $3$

Plant

Capacity

Appleton $$1,400,000$ $$10\mathrm{.}75$ $$10\mathrm{.}60$ $$10\mathrm{.}3030,000$

Oshkosh $$1,220,000$ $$6\mathrm{.}20$ $$7\mathrm{.}10$ $$9\mathrm{.}0517,000$

Omaha $$1,680,000$ $$4\mathrm{.}30$ $$6\mathrm{.}20$ $$7\mathrm{.}5538,000$

Terre Haute $$1,480,000$ $$7\mathrm{.}10$ $$8\mathrm{.}45$ $$5\mathrm{.}2244,000$

Toledo $$1,500,000$ $$8\mathrm{.}55$ $$8\mathrm{.}66$ $$9\mathrm{.}5229,000$

DC Demand $=50,20038,50023,900$

Formulate the model in your document using the headings listed below:

Decision Variables:

Objective Function:

Constraints:

Additional Work for Constraints: