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.$ page $920$Heating and lighting costs equal $$400$ per week of rearing, regardless of which type of fish is being raised. Fixed overhead costs for the year amount to $$80,000.$ Percula can sell clownfish for $$4$ each and angelfish for $$10$ each.

Instructions

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

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

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?

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?