$[30$ points$]$ Sleekfon and Sturdyfon are two major cell phone manufacturers that have recently

merged. Their current market sizes are as shown in Table $5-9.$ All demand is in millions of units.

Sleekfon has three production facilities in Europe $($EU$),$ North America, and South America.

Sturdyfon also has three production facilities in Europe $($EU$),$ North America, and the rest of

Asia$/$Australia$.$ The capacity $($in millions of units$),$ annual fixed cost $($in millions of $$),$ and variable

production costs $($$ per unit$)$ for each plant are as shown in Table $5-10.$ Transportation costs

between regions are as shown in Table $5-11.$ All transportation costs are shown in dollars per unit.

Duties are applied on each unit based on the fixed cost per unit capacity, variable cost per unit,

and transportation cost. Thus, a unit currently shipped from North America to Africa has a fixed

cost per unit of capacity of $$5\mathrm{.}00,$ a variable production cost of $$5\mathrm{.}50,$ and a transportation cost

of $$2\mathrm{.}20.$ The $25$ percent import duty is thus applied on $$12\mathrm{.}70(5\mathrm{.}00+5\mathrm{.}50+2\mathrm{.}20)$ to give a total

cost on import of $$15\mathrm{.}88.$ For the questions that follow, assume that market demand is as in Table

$5-9.$ The merged company has estimated that scaling back a $20-$million$-$unit plant to $10$ million

units saves $30$ percent in fixed costs. Variable costs at a scaled$-$back plant are unaffected. Shutting

a plant down $($either $10$ million or $20$ million units$)$ saves $80$ percent in fixed costs. Fixed costs are

only partially recovered because of severance and other costs associated with a shutdown.

a$.$ What is the lowest cost achievable for the production and distribution network prior to

the merger? Which plants serve which markets?

b$.$ What is the lowest cost achievable for the production and distribution network after the

merger if none of the plants is shut down? Which plants serve which markets?

c$.$ What is the lowest cost achievable for the production and distribution network after the

merger if plants can be scaled back or shut down in batches of $10$ million units of

capacity? Which plants serve which markets?

d$.$ How is the optimal network configuration affected if all duties are reduced to $0?$

e$.$ How should the merged network be configured?

TABLE $5-9$ Global Demand and Duties for Sleekfon and Sturdyfon

TABLE $5-10$ Plant Capacities and Costs for Sleekfon and Sturdyfon

TABLE $5-11$ Transportation Costs Between Regions $($$ per Unit$)$

bys using slover method