A large international computer manufacturer is designing a new model of personal computer. It

estimates that the cost to produce one unit will be around $$700$ and it can sell a unit for $$800.$ It

estimates that the capacity setup for this model will cost $$15$ million.

a$)$ How many units will it need to sell to justify the capacity cost?

b$)$ The manufacturer must decide whether to produce the keyboards internally or to purchase

from an outside supplier. The supplier is willing to sell the keyboards for $$50$ each, but the

manufacturer estimates that it can internally produce the keyboards for $$35$ each. Management

estimates that expanding the current plant and purchasing the necessary equipment to make the

keyboards would cost $$8$ million. Above what demand quantity the expansion should be

considered? Should they undertake the expansion if the expected demand is $0\mathrm{.}6$ million units?

c$)$ The manufacturer decides to produce the keyboards internally for a better production control.

The manufacturer is now evaluating two options for expansion: A$)$ expansion based on ordinary

production equipment at the cost of $$8$ million; and B$)$ expansion based on modern production

equipment that will cost $$10$ million. Through Option $A,$ the keyboard production will cost $$35$

per unit. Production per unit will be $$30$ with Option B$.$ For what ranges of demand quantity each

option is better?