Question $1.$ Determine the utilization and efficiency for each of the following situations.

$1.$ A loan processing operation that processes an average of $7$ loans per day. The operation has a design capacity of $10$ loans per day and an effective capacity of $8$ loans per day.

$2.$ A furnace repair team that services an average of four furnaces a day if the design capacity is six furnaces a day and the effective capacity is five furnaces a day.

True or false. Would you say that systems that have higher efficiency ratios than other systems will always have higher utilization ratios than those other systems? "This is not necessarily true. If the design capacity is relatively high, the utilization could be low even though efficiency was high."

Question $2.$

A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have fixed costs of $$9,200$ per month and variable costs of $70$ cents per unit produced. Each item is sold to retailers at a price that averages $90$ cents.

a$.$ What volume per month is required in order to break even?

b$.$ What profit would be realized on a monthly volume of $61,000$ units?

Question $3.$

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B$,$ have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $$40,000$ for A and $$30,000$ for B; variable costs per unit would be $$10$ for A and $$11$ for B; and revenue per unit would be $$15.$

a$.$ Determine each alternative$$s break$-$even point in units.

b$.$ At what volume of output would the two alternatives yield the same profit?

c$.$ If expected annual demand is $12,000$ units, which alternative would yield the higher profit?