PROBLEM $20\mathrm{.}7$A

Analyzing the Effects of Changes in Costs and Volume

Percula Farms raises marine fish for sale in the aquarium trade. Each year, Percula obtains a batch of approximately one million eggs from a local

supplier. Percula's manager is trying to decide whether to use the farm's facilities to raise Maroon Clownfish or Queen Angelfish. Clownfish eggs

cost $$5,500$ per batch, while angelfish eggs cost $$9,500$ per batch. Due to differences in needs, only one species may be raised at a time and only one

batch of fish can be raised in any $52-$week period.

With current facilities, approximately $10$ percent of clownfish eggs and $5$ percent of angelfish eggs can be successfully raised to maturity.

Clownfish take approximately $35$ weeks to grow to a salable size, while angelfish take $50$ weeks. Angelfish also require more care than clownfish.

Each week, angelfish need two complete water changes and $20$ feedings, while clownfish need only one water change and $15$ feedings. Each feeding

costs $$150$ and each water change costs $$1,000.$ Heating and lighting costs equal $$400$ per week of rearing, regardless of which type page $920$

of fish is being raised. Fixed overhead costs for the year amount to $$80,000.$ Percula can sell clownfish for $$4$ each and angelfish for

$$10$ each.

Instructions

a$.$ Which species should Percula raise to earn the highest operating income for the year?

b$.$ Other than fixed costs, which factors or categories of costs seem to have the greatest influence on operating income?

c$.$ Percula's manager is considering the following improvements, each of which will cost an additional $$8,000$ for the year. Due to resource

limitations$,$ only one can be implemented.

Purchasing a higher quality filter material that will significantly improve water conditions in the rearing tanks. The higher water quality will

increase the survival rates to $12$ percent for clownfish and $6$ percent for angelfish. The need for water changes will also be reduced to one

each week for angelfish. Due to the higher yields, feeding costs will increase to $$160$ each.

Installing newer, more efficient equipment that will reduce heating and lighting costs to $$300$ per week of rearing. The new equipment will

promote more stable conditions, increasing the survival rates of clownfish to $10\mathrm{.}5$ percent and of angelfish to $5\mathrm{.}5$ percent. The slight change

in survival rates is not expected to increase feeding costs.

Using your answers to part $b($with no calculations$),$ which option do you think will be more beneficial?

d$.$ Perform the necessary calculations to check if your answer to part $c$ was correct. Should either of the investments be undertaken, and if so$,$

which fish species should be raised?