Problem
Scenario: Azucar 85 Sons is involved in the sugar business in Florida. The president of the company, Octavio Azucar, goes to a commodity sale once a month where he buys and sells sugar in bulk. Azucar uses a local warehouse for storing his sugar inventory. This warehouse charges $10 per average ton of sugar stored per month (based on the average between the beginning and ending inventory each month). The warehouse guarantees Azucar the capacity to store up to 400 tons of sugar at the end of each month. Azucar estimates the price per ton of sugar in each of the next six months to be $135, $110, $150, $175, $130, and $145, for both buying and selling. Assume Azucar currently has 70 tons of sugar in storage. How many tons of sugar should Azucar buy and sell during each of the next six months to maximize their profit trading this commodity? Write a linear optimization model for this problem and solve it in Excel.
Task
A. What is Azucar's optimal profit?
B. What is their total inventory cost over 6 months?
C. How much revenue did they generate from selling sugar over 6 months?
D. In how many months out of the 6 did their inventory reach its maximum capacity?