Arkansas$).$ Each distribution center can process $($repackage$,$ mark for sale, and ship$)$ at most $500$ skateboards per week.

$\backslash$table$[[$Factory$/$DCs$,$Shipping Costs $($$ per skateboard$)],[$Iowa $4,$Maryland $5,$Idaho $6,$Arkansas $7],[$Detroit $1,25\mathrm{.}00,25\mathrm{.}00,35\mathrm{.}00,40\mathrm{.}00],[$Los Angeles $2,35\mathrm{.}00,45\mathrm{.}00,35\mathrm{.}00,42\mathrm{.}50],[$Austin $3,40\mathrm{.}00,40\mathrm{.}00,42\mathrm{.}50,32\mathrm{.}50]]$

$\backslash$table$[[$Retailers$/$DCs$,$Shipping Costs $($$ per skateboard$),],[$Iowa$,$Maryland,Idaho,Arkansas $7,],[$Just Sports,$8,30\mathrm{.}00,20\mathrm{.}00,35\mathrm{.}00,27\mathrm{.}50],[$Sports $\text{'}$N Stuff,Q$9,27\mathrm{.}50,32\mathrm{.}50,40\mathrm{.}00,25\mathrm{.}00],[$The Sports Dude,$30\mathrm{.}00,40\mathrm{.}00,32\mathrm{.}50,42\mathrm{.}50,]]$

$($a$)$ Draw the network representation for this problem. $($Submit a file with a maximum size of $1$ MB $.)$

Choose File no file selected represents the number of units shipped from node $i$ to node $j.)$

Min

s$.$t$.$

Detroit Production

Los Angeles Production

Austin Production

Iowa Shipments

Maryland Shipments

Idaho Shipments

Arkansas Shipments

Iowa Processing

Maryland Processing

Idaho Processing

Arkansas Processing

Just Sports Demand

Sports Stuff Demand

Sports Dude Demand

$x_{ij}0$ for all i and $j.$

What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where $x_{ij}$ represents the number of units shipped from node $i$ to node $j.$

$\left[\begin{array}{cccc}{x}_{14}& x_{15}& x_{16}& x_{17}\\ x_{24}& x_{25}& x_{26}& x_{27}\\ x_{34}& x_{35}& x_{36}& x_{37}\\ x_{48}& x_{58}& x_{68}& x_{78}\\ x_{49}& x_{59}& x_{69}& x_{79}\\ x_{410}& x_{510}& x_{610}& x_{710}\end{array}\right]=\left[\begin{array}{c}\\ \end{array}\right]$

What is the minimum attainable transportation cost $($in dollars$)?$

$ per week? $($Assume $50$ operating weeks per year.$)$

The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ per week. Therefore, the potential savings over $50$ weeks is per year. The $$40,000$ cost of expansion $])$ the potential savings, so Sports of All Sorts $()$ expand.

Arkansas$).$ Each distribution center can process $($repackage$,$ mark for sale, and ship$)$ at most $500$ skateboards per week.

$\backslash$table$[[$Factory$/$DCs$,$Shipping Costs $($$ per skateboard$),],[$Iowa$,$Maryland,Idaho,Arkansas,$],[$Detroit$,25\mathrm{.}00,25\mathrm{.}00,35\mathrm{.}00,40\mathrm{.}00,],[$Los Angeles,$2,35\mathrm{.}00,45\mathrm{.}00,35\mathrm{.}00,42\mathrm{.}50],[$Austin$,3,40\mathrm{.}00,40\mathrm{.}00,42\mathrm{.}50,32\mathrm{.}50]]$

$\backslash$table$[[$Retailers$/$DCs$,$Shipping Costs $($$ per skateboard$)],[$Maryland$,$Idaho,Arkansas,$],[$Just Sports,$3,30\mathrm{.}00,20\mathrm{.}00,35\mathrm{.}00,27\mathrm{.}50],[$Sports $\text{'}$N Stuff,$9.,27\mathrm{.}50,32\mathrm{.}50,40\mathrm{.}00,25\mathrm{.}00],[$The Sports Dude,$30\mathrm{.}00,40\mathrm{.}00,32\mathrm{.}50,42\mathrm{.}50,]]$

$($a$)$ Draw the network representation for this problem. $($Submit a file with a maximum size of $1$ MB $.)$

Choose File nofile selected represents the number of units shipped from node $\frac{?}{?}$ to node $j.)$

Min

s$.$t$.$

Detroit Production

Los Angeles Production

Austin Production

Iowa Shipments

Maryland Shipments

Idaho Shipments

Arkansas Shipments

Iowa Processing

Maryland Processing

Idaho Processing

Arkansas Processing

Just Sports Demand

Sports Stuff Demand

Sports Dude Demand

$x_{ij}0$ for all $/$ and $j.$

What is the minimum attainable transportation cost $($in dollars$)?$

$ per week? $($Assume $50$ operating weeks per year.$)$

The cost of the optimal solution associated with this increased capacity at the lowa distribution center is : ser week. Therefore, the potential savings over $50$ weeks is $50,-1,$ per year. The $$40,000$ cost of expansion the potential savings, so Sports of All Sorts expand.Arkansas$).$ Each distribution center can process $($repackage$,$ mark for sale, and ship$)$ at most $500$ skateboards per week.

$\backslash$table$[[$Factory$/$DCs$,$Shipping Costs $($$ per skateboard$)],[$Iowa $4,$Maryland $5,$Idaho $6,$Arkansas $7],[$Detroit $1,25\mathrm{.}00,25\mathrm{.}00,35\mathrm{.}00,40\mathrm{.}00],[$Los Angeles $2,35\mathrm{.}00,45\mathrm{.}00,35\mathrm{.}00,42\mathrm{.}50],[$Austin $3,40\mathrm{.}00,40\mathrm{.}00,42\mathrm{.}50,32\mathrm{.}50]]$

$\backslash$table$[[$Retailers$/$DCs$,$Shipping Costs $($$ per skateboard$),],[$Iowa$,$Maryland,Idaho,Arkansas $7,],[$Just Sports,$8,30\mathrm{.}00,20\mathrm{.}00,35\mathrm{.}00,27\mathrm{.}50],[$Sports $\text{'}$N Stuff,Q$9,27\mathrm{.}50,32\mathrm{.}50,40\mathrm{.}00,25\mathrm{.}00],[$The Sports Dude,$30\mathrm{.}00,40\mathrm{.}00,32\mathrm{.}50,42\mathrm{.}50,]]$

$($a$)$ Draw the network representation for this problem. $($Submit a file with a maximum size of $1$ MB $.)$

Choose File no file selected represents the number of units shipped from node $i$ to node $j.)$

Min

s$.$t$.$

Detroit Production

Los Angeles Production

Austin Production

Iowa Shipments

Maryland Shipments

Idaho Shipments

Arkansas Shipments

Iowa Processing

Maryland Processing

Idaho Processing

Arkansas Processing

Just Sports Demand

Sports Stuff Demand

Sports Dude Demand

$x_{ij}0$ for all i and $j.$

What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where $x_{ij}$ represents the number of units shipped from node $i$ to node $j.$

$\left[\begin{array}{cccc}{x}_{14}& x_{15}& x_{16}& x_{17}\\ x_{24}& x_{25}& x_{26}& x_{27}\\ x_{34}& x_{35}& x_{36}& x_{37}\\ x_{48}& x_{58}& x_{68}& x_{78}\\ x_{49}& x_{59}& x_{69}& x_{79}\\ x_{410}& x_{510}& x_{610}& x_{710}\end{array}\right]=\left[\begin{array}{c}\\ \end{array}\right]$

What is the minimum attainable transportation cost $($in dollars$)?$

$ per week? $($Assume $50$ operating weeks per year.$)$

The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ per week. Therefore, the potential savings over $50$ weeks is per year. The $$40,000$ cost of expansion $])$ the potential savings, so Sports of All Sorts $()$ expand.

Arkansas$).$ Each distribution center can process $($repackage$,$ mark for sale, and ship$)$ at most $500$ skateboards per week.

$\backslash$table$[[$Factory$/$DCs$,$Shipping Costs $($$ per skateboard$),],[$Iowa$,$Maryland,Idaho,Arkansas,$],[$Detroit$,25\mathrm{.}00,25\mathrm{.}00,35\mathrm{.}00,40\mathrm{.}00,],[$Los Angeles,$2,35\mathrm{.}00,45\mathrm{.}00,35\mathrm{.}00,42\mathrm{.}50],[$Austin$,3,40\mathrm{.}00,40\mathrm{.}00,42\mathrm{.}50,32\mathrm{.}50]]$

$\backslash$table$[[$Retailers$/$DCs$,$Shipping Costs $($$ per skateboard$)],[$Maryland$,$Idaho,Arkansas,$],[$Just Sports,$3,30\mathrm{.}00,20\mathrm{.}00,35\mathrm{.}00,27\mathrm{.}50],[$Sports $\text{'}$N Stuff,$9.,27\mathrm{.}50,32\mathrm{.}50,40\mathrm{.}00,25\mathrm{.}00],[$The Sports Dude,$30\mathrm{.}00,40\mathrm{.}00,32\mathrm{.}50,42\mathrm{.}50,]]$