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Problem $1$: The Medequip Company Shipping

The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month$$s production output. The following table shows the cost of shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer.

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A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer.

a$)$ Develop the spreadsheet model to solve this problem. Show the model.

b$)$ Use the Linear Programming Excel solver and determine the optimal solution.

Problem $2$: Optimal Grain Allocation for HarvestField

HarvestField is a leading agricultural entity specializing in grain cultivation, possessing three extensive grain farms located in central Nebraska, specifically in the towns of Sunville, Grainland, and Fieldtown. The current grain reserves are as follows: Sunville has $275,000$ bushels, Grainland has $400,000$ bushels, and Fieldtown holds $300,000$ bushels.

HarvestField operates grain milling facilities in Northport, Midcity, and Southville, each with milling capacities of $200,000,600,000,$ and $225,000$ bushels, respectively. HarvestField has contracted a local logistics firm that charges based on the distance covered for each bushel to transfer the grain from the farms to the mills. The distance a single bushel of grain covers is termed as a bushel$-$mile. The table below outlines the