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 $$5\mathrm{.}00(=100/20$ from Table $5-9),$ a variable production cost of $$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 $5-8.$

$$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.

What is the lowest cost achievable for the production and distribution network prior to the merger? Which plants serve which markets?

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?