One of the necessary changes was to renovate and replace equipment. Partially based on

making the right choice regarding process and capacity, their $7-$year loan was repaid in $3$ years.

Assume the following scenario: To increase capacity in their retail area by replacing equipment,

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 cone would be $$1\mathrm{.}10$ for A and $$1\mathrm{.}60$ for B; and revenue per ice cream cone is $$3\mathrm{.}50.$

A new production line has three stations $$ mixing the base ingredients followed by freezing

followed by packaging. The first station $($mixing the base ingredients$)$ can process a batch in

$11$ minutes. The second station $($freezing$)$ has two identical machines, each of which can

process a batch in $13$ minutes. The third station $($packaging$)$ can process a batch in $9$ minutes.

What is the break$-$even point for alternative A in number of ice cream cones? $($round to nearest

whole number$)$

What is the break$-$even point for alternative B in number of ice cream cones? $($round to nearest

whole number$)$

What is the total revenue for alternative A at the break$-$even point?

What is the capacity of the bottleneck station? $($batches$/$hour; round to $2$ decimals$)$

What is the throughput time for a specific batch $($in minutes$)?$

If the production line operates $10$ hours per day, $5$ days per week, what is its weekly

capacity? $($batches$/$week$,$ nearest whole number$)$

If the weekly capacity in the previous question is considered effective capacity and efficiency

has historically been $80\%,$ what is the actual output $($batches$/$wk$,$ round to the nearest whole

number$)?$

Using information from the previous question, what is the utilization $\%$ if design capacity is $400$

batches$/$week$?(\%$ rounded to nearest $1$ decimal, such as $22\mathrm{.}2\%)$

What is the relationship of the two machines at the freezing station?