$2.$ A manager is trying to decide whether to purchase a certain part or to have it produced

internally. Internal production could use either of two processes. One would entail a

variable cost of $$17$ per unit and an annual fixed cost of $$200,000$; the other would entail

a variable cost of $$14$ per unit and an annual fixed cost of $$240,000.$ Three vendors are

willing to provide the part. Vendor A has a price of $$20$ per unit for any volume up to

$30,000$ units. Vendor B has a price of $$22$ per unit for demand of $1,000$ units or less, and

$$18$ per unit for larger quantities. Vendor C offers a price of $$21$ per unit for the first

$1,000$ units, and $$19$ per unit for additional units. a$.$ If the manager anticipates an annual volume of $20,000$ units, which alternative

would be best from a cost standpoint? For $30,000$ units, which alternative would

be best?

b$.$ Determine the range for which each alternative is best. Are there any alternatives

that are never best? Which? $4.$ The following diagram shows a four$-$step process that begins with Operation $1$ and ends

with Operation $4.$ The rates shown in each box represent the effective capacity of that

operation.

a$.$ Determine the capacity of this process.

b$.$ Which action would yield the greatest increase in process capacity: $(1)$ increase

the capacity of Operation $1$ by $15$ percent; $(2)$ increase the capacity of Operation $2$

by $10$ percent; or $(3)$ increase the capacity of Operation $3$ by $10$ percent?

The manager of a car wash must decide whether to have one or two wash lines. One line

will mean a fixed cost of $$7,000$ a month, and two lines will mean a fixed cost of $$11,500$

a month. Each line would be able to process $15$ cars an hour. Variable costs will be $$2$ per

car, and revenue will be $$6\mathrm{.}50$ per car. The manager projects an average demand of

between $14$ and $18$ cars an hour. Would you recommend one or two lines? The car wash

is open $300$ hours a month.

The following diagram shows a four$-$step process that begins with Operation $1$ and ends

with Operation $4.$ The rates shown in each box represent the effective capacity of that

operation.

a$.$ Determine the capacity of this process.

b$.$ Which action would yield the greatest increase in process capacity: $(1)$ increase

the capacity of Operation $1$ by $15$ percent; $(2)$ increase the capacity of Operation $2$

by $10$ percent; or $(3)$ increase the capacity of Operation $3$ by $10$ percent?