1. (30 points) For this question use the Excel file provided. A company ships their products from three different plants (one in Los Angeles, one in Atlanta, and one in New York City) to four regions of the United States (East, Midwest, South, West). Each plant has a limited capacity on how many products can be sent out, and each region has a demand of products that they must receive. There is a different unit transportation cost between each plant, or each city, and each region. The company wants to determine how many products each plant should ship to each region in order to minimize the total transportation cost. East Midwest South West $5.00 $3.50 $4.20 $2.20 Los Angeles Atlanta Plant capacity 10,000 12,000 $3.20 $2.60 $1.80 $4.80 New York City $2.50 $3.10 $3.30 $5.40 14,000 Regional demand 9,000 6,000 6,000 13,000 Objective function How do we measure the cost of a complete solution? (Hint: write a function that measures transportation costs with the decision variables above and the given unit shipment costs.) Complete the partial function below. Minimize z = $5.0X2 + $3.5X2 + $4.2X2 + ... Constraints How do we limit the decision variables so that we get feasible solutions, where all demand is satisfied and capacity not exceeded? Demand at all regions have to be satisfied (one for each region.) Complete the rest of the table. Total received from all plants X1 + X5 + X9 Total demanded 9,000 Region East Midwest South West Capacity cannot be exceeded at any plant (one for each plant.) Complete the rest of the table. Plant Total shipped to all plants Total capacity Los Angeles X1 + X2 + X3 + X4 10,000 Atlanta New York City