There are $3$ potential sites for consideration for building a distribution center to ship to $3$ customer zones. Like the example we have solved in Excel, the information regarding demand at each customer zone, shipping cost from a potential distribution centre to a customer zone, and fixed cost of building a distribution center at each location with a certain capacity is provided in the table below. Each distribution, if built, can operate at either the capacity level of $25,000($small size$)$ or $75,000($extra large size$).$ Using Solver in Excel, solve this Capacitated Plan Location problem and select the correct answer from the following choices.

Potential Customer $1$ Customer $2$ Customer $3$ Fixed Cost Fixed Cost

Site Medium Large

$---------------------------------------------------------------------------------------------------------------------$

Site $1150170139120,000240,000$

Site $2120135107150,000400,000$

Site $3240245230200,000390,000$

$---------------------------------------------------------------------------------------------------------------------$

Demand $12,00023,00040,000$

Select one:

a$.$

The optimal objective function value is $$5,450,000.$

b$.$

The optimal objective function value is $$5,225,000.$

c$.$

The optimal objective function value is $$7,450,000.$

d$.$

None of the choices.

e$.$

The optimal objective function value is $$9,225,000.$

f$.$

The optimal objective function value is $$3,225,000.$

g$.$

The optimal objective function value is $$995,000.$

h$.$

The optimal objective function value is $$6,450,000.$

i$.$

The optimal objective function value is $$8,450,000.$