True Machines, Inc. would like to develop a plan for building and shipping their Premium Generator product to satisfy customer orders. The Murrysville plant can produce $17$ units and the Erie plant can produce $21$ units. Three customers have entered orders as follows:

Oil City Refinery $10$ units

Gas Blasters $15$ units

Energy Products $13$ units

Shipping costs are as follows:

Shipping Cost Per Unit Oil City Refinery Gas Blasters Energy Products

Murrysville $$750$ $$950$ $$800$

Erie $$900$ $$900$ $$600$

Develop a mathematical and Excel model to generate the minimum cost shipping solution.