$4)$ Zippy City Bikes is planning to place collection & charging $($C&C$)$ centers for its electric bikes in five neighborhoods of Cleveland, Ohio: $(1)$ Ohio City, $(2)$ Gordon Square, $(3)$ Downtown, $(4)$ Lakewood, and $(5)$ Tremont. The firm would also like these charging stations to be close to the three areas that customers frequently travel: $($X$)$ Edgewater Park, $($Y$)$ Rock & Roll Hall of Fame, and $($Z$)$ West Side Market. At the end of each day, Zippy City Bikes needs to pick up the bikes from the three areas of interest$$Edgewater$,$ Rock & Roll Hall of Fame, and West Side Market$$and transfer them to the C&Cs$.$ The per$-$unit cost of transferring bikes from the areas of interest to the C&C are given in the below table. For example, the firm incurs a per bike cost of $$35$ when a bike is transferred from Edgewater Park to Ohio City.

Net cost per bike from Area of Interest X

Region X Y Z

$1353545$

$2453045$

$3706050$

$4204525$

$5654545$

The firm predicts $40,25,$ and $35$ bikes to be left at the three areas of interest at the end of the day, respectively. The firm would also like to decide which C&C center$($s$)$ to open. The maximum number of bikes that can be placed in each C & C center and the associated construction costs are:

C&C Center C & C Center Capacity Construction Cost$($$$)$

$125$ $$13,250$

$225$ $$11,000$

$325$ $$15,000$

$425$ $$12,000$

$525$ $$14,000$

The firm would like to find which C&Cs to open and a minimum cost plan to transfer the bikes from areas of interest to C&Cs$.$

a$.$ Write the mathematical formulation.

b$.$ Solve using excel solver.Net Cost Per Unit