SCM 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 Oshkosh 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 $$500,000$ $$7\mathrm{.}75$ $$9\mathrm{.}60$ $$8\mathrm{.}3039,000$

Oshkosh $$420,000$ $$7\mathrm{.}20$ $$7\mathrm{.}10$ $$8\mathrm{.}0511,000$

Omaha $$680,000$ $$6\mathrm{.}30$ $$6\mathrm{.}20$ $$7\mathrm{.}5529,000$

Terre Haute $$580,000$ $$8\mathrm{.}10$ $$8\mathrm{.}45$ $$5\mathrm{.}2245,000$

Toledo $$600,000$ $$7\mathrm{.}92$ $$8\mathrm{.}34$ $$9\mathrm{.}2528,000$

DC Demand $=48,50046,50017,900$

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

Decision Variables:

Objective Function:

Constraints:

Additional Work for Constraints: