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A Firm Has 4 Plants That Produce Widgets The Firm Needs to Satisfy All Demand Each Day, but B

question 58

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A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below:
Shipping CostsCustomerper unit Plant123A$25$35$15 B$20$30$40C$40$35$20D$15$20$25\begin{array}{c}Shipping~ Costs&&&Customer\\per~unit~Plant&&1&2&3\\\mathrm{A} && \$ 25 & \$ 35 & \$ 15 \\\mathrm{~B} && \$ 20 & \$ 30 & \$ 40 \\\mathrm{C} && \$ 40 & \$ 35 & \$ 20 \\\mathrm{D} && \$ 15 & \$ 20 & \$ 25\end{array}
The firm needs to satisfy all demand each day, but would like to minimize the total costs.
The firm's problem falls within which classification?

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Definitions:

Old Northwest

A historical term for the territorial region of the United States northwest of the Ohio River, encompassing states like Ohio, Indiana, Illinois, Michigan, Wisconsin, and parts of Minnesota.

Mississippi River

One of the largest river systems in North America, flowing southwards for over 2,300 miles from its source in Minnesota to the Gulf of Mexico, serving as a vital waterway for transportation, commerce, and ecology.

Treaty

A formal and legally binding agreement between two or more sovereign states or international organizations.

War of 1812

The War of 1812 was a conflict fought between the United States and Britain over issues including trade restrictions and the impressment of American sailors, culminating in no significant territorial changes.

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