Hansen Controls has been awarded a contract for a large number of control panels. To meet this demand, it will use its existing plants in San Diego and Houston, and consider new plants in Tulsa, St$.$ Louis, and Portland. Finished control panels are to be shipped to Seattle, Denver, and Kansas City. Pertinent information is given in the table$\backslash$table$[[,$Shipping Cost to Destination$],[$Sources$,$Construction Cost,Seattle,Denver,Kansas City,Capacity$],[$San Diego,$---,5,7,8,2,500],[$Houston$,---,10,8,6,2,500],[$Tulsa$,350,000,9,4,3,10,000],[$St$.$ Louis,$200,000,12,6,2,10,000],[$Portland$,480,000,4,10,11,10,000],[,$Demand,$3,000,8,000,9,000,]]$

a$)$ Develop an optimization model whose solution would reveal which plants to build and the optimal shipping schedule. In other words, clearly define the decision variables, write the objective function and the constraints in terms of these variables.

b$)$ Develop the spreadsheet model. Solve the model using Excel Solver and provide your recommendation.