whirlpool Inc., is a manufacturer of refrigerators that has seen its demand grow significantly. The company anticipates nationwide demand for the next year to be $180,000$ units in the South, $120,000$ units in the Midwest, $110,000$ units in the East, and $100,000$ units in the West. Managers at whirlpool are designing the manufacturing network and have selected four potential sites$-$New York, Atlanta, Chicago, and San Diego 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 $5-6,$ along with the cost of producing and shipping a refrigerator to each of the four markets. TABLE $5-6$ Production and Transport Costs for whirlpool, Inc. New York Atlanta Chicago San diego Annual fixed cost $$6$ million $$5\mathrm{.}5$ million $$5\mathrm{.}6$ million $$6\mathrm{.}1$ million of $200,000$ plant Annual fixed cost $$10$ million $$9\mathrm{.}2$ million $$9\mathrm{.}3$ million $$10\mathrm{.}2$ million of $400,000$ plant Annual fixed cost East $$211$ $$232$ $$238$ $$299$ South $$232$ $$212$ $$230$ $$280$ Midwest $$240$ $$230$ $$215$ $$270$ West $$300$ $$280$ $$270$ $$225$

Using excel and solver, develop a linear programming model that answers the following questions:

$1.$ Where should Whirlpool Inc. build its plant facilities?

$2.$ How large in terms of capacity should each facility be$?$

$3.$ What is the total cost for the optimal solution?