$1.$ Write down the Linear Programming Model using the Summation Notation that would provide a concise description of the following components of the LP Model: A$.$ Objective Function B$.$ Constraints C$.$ Decision Variables D$.$ Input Data Hint: You can use similar mathematical formulation to that used in the Capacitated Plant Location Model described on Page $114.2.$ Use the attached excel file as an aid to find the optimal distribution strategy that minimizes the cost of the supply chain network. $2.$ Drylce, Inc., is a manufacturer of air conditioners 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 Drylce are designing the manufacturing network and have selected four potential sites $$ New York, Atlanta, Chicago, and San Diego. Plants could have a capacity of either $200,000$ or $400,000$ units. The annual fixed costs at the four locations are shown in Table $5-50,$ along with the cost of producing and shipping an air conditioner to each of the four markets. Where should Drylce build its factories and how large should they be$?$ Table $5-5$ Production and Transport Costs for Drylce, Inc. New York Atlanta Chicago San Diego Annual fixed cost of $200,000$ plant $$6$ million $$5\mathrm{.}5$ million $$5\mathrm{.}6$ million $$6\mathrm{.}1$ million Annual fixed cost of $400,000$ plant $$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$ DryIce Inc. Facilities Planning from from San Shipped from NY Shipped from Atlanta Unmet Demand New York Atlanta Chicago Chicago San Diego Diego Requirements Fixed Costs $200$k $400$k $6,000,00010,000,0005,500,0009,200,0005,600,0009,300,0006,100,00010,200,000238299230$ Variable Costs East South Midwest West Small $(2002)(1=$open$)$ Large $(400$k$)(1=$open$)$ Capacity$/$Cost $211232240300232212230280215110,000180,000120,000100,000280270225270$ Binary Integer Variables Decision Variable Cells $($Shipped Units$)$ LHS of Demand Constraints LHS of Supply Constraints Objective Function $($Compont $1,$ Component xcess Capacity TOTAL SYSTEM COST$-$Objective Function Cells that are changed All non$-$negative integers