Question $1$ Gator Electric, Inc., is a manufacturer of refrigerators that has seen its demand grow significantly. The company anticipates nationwide demand for the next year to be $110,000$ units in the East, $180,000$ units in the South, $100,000$ units in the Midwest, and $120,000$ units in the West. Managers at Gator Electric are designing the manufacturing network and have selected four potential sites$-$ Philadelphia, Atlanta, Minneapolis, and Portland. Plants could have a capacity of either $200,000$ or $400,000$ units. The annual fixed costs at the four locations are shown in Table $1.$ Along with the cost of producing and shipping a refrigerator to each of the four markets. Where should a refrigerator to each of the four markets. Where should Gator Electric build its factories and how large should they be$?$ a$.$ Write the model including the objective function, the decision variables, and the constraints. $(30$ points$)$ b$.$ Solve the problem in Excel. Provide your model in Excel including the constraints in Excel solver, the solution, and the total cost. $(20$ points$)$ Table $1$ Production and Transport Costs for Gator Electric Philadelphia Atlanta Minneapolis Portland $$6$ million $$5\mathrm{.}5$ million $$5\mathrm{.}6$ million $$6\mathrm{.}1$ million Annual fixed cost of $200,000$ plant Annual fixed cost of $400,000$ plant $$10$ million $$9\mathrm{.}2$ million $$9\mathrm{.}3$ million $$10\mathrm{.}2$ million East $$211$ $$232$ $$238$ $$299$ South $$232$ $$212$ $$230$ $$280$ Midwest $$240$ $$230$ $$215$ $$270$ West $$300$ $$280$ $$270$ $$225$