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The Following Table Shows the Unit Shipping Cost Between Cities

question 24

Essay

The following table shows the unit shipping cost between cities, the supply at each origin city, and the demand at each destination city. Solve this minimization problem using the transportation simplex method and compute the optimal total cost.  Destination  Origin  Terre Haute  Indianapolis  Ft. Wayne  South Bend  Supply  St. Louis 86129100 Evansville 55108100 Bloomington 32910100 Demand 150604545\begin{array} { l | c c c c | c } &&&{ \text { Destination } } & \\\text { Origin } & \text { Terre Haute } & \text { Indianapolis } & \text { Ft. Wayne } & \text { South Bend } & \text { Supply } \\\hline \text { St. Louis } & 8 & 6 & 12 & 9 & 100 \\\text { Evansville } & 5 & 5 & 10 & 8 & 100 \\\text { Bloomington } & 3 & 2 & 9 & 10 & 100 \\\hline \text { Demand } & 150 & 60 & 45 & 45 &\end{array}

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Definitions:

Break-Even Analysis

An analytical process to determine at what point a business neither makes a profit nor incurs a loss, calculated by equating total costs with total revenues.

Production Supervisor

A production supervisor is responsible for overseeing the daily operations of manufacturing plants, ensuring that production schedules are met and quality standards are maintained.

Fixed Cost

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance.

Sales Mix

The composition of different products or services sold by a company, affecting its overall profitability.

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