Problem III. Transportation Model Company A has four plants locating in different cities across the region. There are three markets the company is selling its products to. Currently, each plant can only produce 500 units of products, and Market 1 needs 800 units of the product, Market 2 needs 500 units, while Market 3 needs 500 units. The shipping costs for Company A to ship one unit from each plant to different markets are listed in the following table. Please create (write down in standard format) a LP model and use Excel Solver to find the optimal shipping strategy for Company A, which minimize the total shipping costs.

\begin{tabular}{l|ccc|} \multicolumn{4}{c}{ Unit Shipping Cost (in \$) } \\ \hline & Market 1 & Market 2 & Market 3 \\ \hline Plant 1 & $10 & $8 & $15 \\ Plant 2 & $8 & $9 & $7 \\ Plant 3 & $12 & $13 & $15 \\ Plant 4 & $11 & $10 & $12 \\ \hline \end{tabular}