Question

SHOW ALL WORK! IF YOU USE EXCEL EXPLAIN THE EQUATIONS OR SHOW THEM!!!! please

"Florida Citrus Inc. (FCI) produces and sells a sport drink in the North American market. For years, it has sold in the Asian market through a Tokyo-based importer. The contract with the importer is up for renewal, and FCI decides to reconsider its Asian strategy. After much analysis, it decides that three alternatives warrant further consideration.
OPTION1: STAY WITH THE IMPORTER.
Sell through the current importer who manages all the marketing and distribution of FCI's sport drink in the Asian market. The cost for FCI to produce a barrel in the U.S. and ship it to Japan is $100 per barrel. There are no fixed costs. The importer pays FCI $120 per barrel sold in the Asian market.
OPTION 2: MOVE TO PRODUCTION LICENSING.
License production of FCI drinks to a Japanese beverage firm who also will manage marketing and distribution. This firm will charge FCI a fixed fee of $5.8 million each year to cover its costs of maintaining the quality of FCI products. It will pay FCI $38 per barrel sold in the Asian market.
OPTION 3: TURN TO SELF PRODUCTION.
FCI purchased a fully operational beverage plant from a Japanese company with excess capacity. FCI has already spent $4.5 million to retrofit the beverage plant. The annual fixed costs of operating the plant are $25 million (which does not include the previously spent $4.5 million retrofit cost), and the variable cost is $50 per barrel. FCI will sell to independent wholesalers in Asia at $157 per barrel.

The most profitable option depends on how many barrels FCI will sell in Asia. What is the maximum number of barrels that FCI can sell for option 1 to be the best option?"

Correct Answer: Between 284482.0 and 290230.0

Answer 1

Let amount of drink sold = Q

Profit function of Option1:

Pr1 = Q (120-100)

Profit function of Option 2:

Pr2 = Q * 38 - 5,800,000

Profit function of Option1:

Pr3 = Q (157 - 50) - 25,000,000

For Option 1 to be profitable, Pr1 must be greater than both Pr2 and Pr3.

Pr1>Pr2

Q (120-100) > Q * 38 - 5,800,000

Q < 322,222.2

Now, Pr1 > Pr3

Q (120-100) >  Q (157 - 50) - 25,000,000

Q < 287,356.32

Hence, For Option 1 to be profitable the annual quantity sold must be less than 287356.32 barrels.