PLEASE SOLVE USING EXCEL AND THE SOLVER FUNCTION. DO NOT SOLVE ANY OTHER WAYAn electrical components company produces capacitors at three locations: Los Angeles, Chicago, and New York.

Capacitors are shipped from these locations to public utilities in five regions of the country: Northeast $($NE$),$

Northwest $($NW$),$ Midwest $($MW$),$ Southeast $($SE$),$ and Southwest $($SW$).$ The cost of producing and shipping a capacitor

from each plant to each region of the country is given in the file ElectricalComponentsData.xlsx$.$ Each plant has an

annual production capacity of $100,000$ capacitors. Each year, each region of the country must receive the following

number of capacitors: NE$,55,000$; NW$,50,000$; MW$,60,000$; SE$,60,000$; SW$,45,000.$ The company believes that

shipping costs are too high, and it is therefore considering building one or two more production plants. Possible sites

are Atlanta and Houston. The costs of producing a capacitor and shipping it to each region of the country are given in

the same file. It costs $$3$ million $($in current dollars$)$ to build a new plant, and operating each plant incurs a fixed cost $($in

addition to variable shipping and production costs$)$ of $$50,000$ per year. A plant at Atlanta or Houston will have the

capacity to produce $100,000$ capacitors per year. Assume that future demand patterns and production costs will

remain unchanged. If costs are discounted at a rate of $12\%$ per year, how can the company minimize the net present

value $($NPV$)$ of all costs associated with meeting current and future demands?

Hints:

It costs $$3$ million $($in current dollars$)$ to build a new plant

Operating each new plant incurs a fixed cost $($in addition to variable shipping and production costs$)$ of $$50,000$ per

year. $($You could include this for existing plants as well or simply ignore it for the existing ones, since being a fixed

cost$,$ it will not impact your decision variables.$)$

To compute the NPV of annually recurring costs for an unknown extended future you can use the following

approach:

Interest rate $=r$

Discount factor $=(\frac{1}{1}+r)$

Factor for calculating NPV $=(1/1-$Discount Factor$)$

So$,$ you can multiply annually recurring costs in the future by this factor to compute their NPV$.$

Finally, we are simply comparing $4$ different scenarios: No new plants, open a new plant in Atlanta, open a new

plant in Houston, open two new plants $($i$.$e$.$ one in Atlanta and one in Houston$).$ You could solve four different

optimization models $($all in a separate excel worksheet$)$ or find a creative way to develop a single model that can

include all these four options in one optimization model.

Unit shipping costs at current locations

To

NE

From

NY

$$27\mathrm{.}86$

NW

$$4\mathrm{.}00$

MW

$$20\mathrm{.}54$

$$2\mathrm{.}00$

$$8\mathrm{.}02$

SE

$$21\mathrm{.}52$

$$6\mathrm{.}74$

$$8\mathrm{.}41$

SW

$$13\mathrm{.}87$

$$10\mathrm{.}67$

$$15\mathrm{.}20$

Unit shipping costs at potential new locations