Im having a hard time understanding where to begin with this question. Can you assist in providing a step by step explanation, preferably utilizing Excel for this problem? $1.$ Fixed Cost $-$ The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

$$ Detroit $=$ $$150,000$

$$ Toledo $=$ $$325,000$

$$ Denver $=$ $$400,000$

$$ Kansas City $=$ $$525,000$

$2.$ Capacities

$$ Detroit $=10,000$ Units

$$ Toledo $=20,000$ Units

$$ Denver $=30,000$ Units

$$ Kansas City $=40,000$ Units

$3.$ Demand $-$ The company's long$-$range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows.

$$ Boston $=20,000$ Units

$$ Atlanta $=30,000$ Units

$$ Houston $=30,000$ Units

$4.$ Shipping Cost $-$ The shipping cost per unit from each plant to each distribution center is as follows.

$$ Detroit to Boston $=$ $$5$

$$ Detroit to Atlanta $=$ $$2$

$$ Detroit to Houston $=$ $$3$

$$ Toledo to Boston $=$ $$4$

$$ Toledo to Atlanta $=$ $$3$

$$ Toledo to Houston $=$ $$4$

$$ Denver to Boston $=$ $$9$

$$ Denver to Atlanta $=$ $$7$

$$ Denver to Houston $=$ $$5$

$$ Kansas City to Boston $=$ $$10$

$$ Kansas City to Atlanta $=$ $$4$

$$ Kansas City to Houston $=$ $$2$

$$ St$.$ Louis to Boston $=$ $$8$

$$ St$.$ Louis to Atlanta $=$ $$4$

$$ St$.$ Louis to Houston $=$ $$3$

the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

The company's long$-$range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows

The shipping cost per unit from each plant to each distribution center is as follows.

Min

s$.$t$.$

Detroit Capacity

Toledo Capacity

Denver Capacity

Kansas City Capacity

St$.$ Louis Capacity

Boston Demand

Atlanta Demand

Houston Demand

$x_{ij}0$ for all i and $j$ and $y_1,y_2,y_3,y_4$ binary

$($b$)$ Solve the model you formulated in part $($a$).$ What is the optimal cost $($in $ $)?$

$ $]$

What is the optimal set of plants to open? $($Select all that apply.$)$

Detroit

Toledo

$$ Denver

Kansas City

$($c$)$ Using equation $(15\mathrm{.}1),$

$($Sum of variables in the set $O)-($sum of variables in the set $Z)($number of variables in the set $O)-1$

$