Question

Zing Coffee Company produces Columbian coffee in batches of 5,500 pounds. The standard quantity of materials required in the process is 5,500 pounds, which cost $6.00 per pound. Columbian coffee can be sold without further processing for $6.40 per pound. Columbian coffee can also be processed further to yield Decaf Columbian, which can be sold for $12.00 per pound. The processing into Decaf Columbian requires additional processing costs of $13,750 per batch. The additional processing will also cause a 4% loss of product due to evaporation.

Determine the price of Decaf Columbian that would cause neither an advantage nor a disadvantage for processing further and selling Decaf Columbian. Round your answer to the nearest cent.

Answer 1

To determine the price of Decaf Columbian that would cause neither an advantage nor a disadvantage for processing further and selling Decaf Columbian, we need to compare the revenues and costs of selling Columbian coffee without further processing versus processing it into Decaf Columbian and selling it.

First, let's calculate the revenue from selling Columbian coffee without further processing:

Revenue from selling Columbian coffee = 5,500 pounds x $6.40 per pound = $35,200

Next, let's calculate the revenue from processing Columbian coffee into Decaf Columbian and selling it:

Amount of Decaf Columbian produced = 5,500 pounds - (0.04 x 5,500 pounds) = 5,280 pounds

Revenue from selling Decaf Columbian = 5,280 pounds x Price per pound

The additional processing cost of $13,750 is a fixed cost that does not depend on the price of Decaf Columbian. So, the total cost of processing and selling Decaf Columbian is:

Total cost of processing and selling Decaf Columbian = $13,750 + 5,500 pounds x $6.00 per pound x 0.04

Total cost of processing and selling Decaf Columbian = $13,750 + $1,320 = $15,070

Now we can set up an equation to find the price of Decaf Columbian that would cause neither an advantage nor a disadvantage for processing further and selling Decaf Columbian:

Revenue from selling Decaf Columbian = Revenue from selling Columbian coffee

5,280 pounds x Price per pound = $35,200

Price per pound = $35,200 / 5,280 pounds

Price per pound = $6.6667 (rounded to 4 decimal places)

So, the price of Decaf Columbian that would cause neither an advantage nor a disadvantage for processing further and selling Decaf Columbian is $6.67 per pound (rounded to the nearest cent).