For the Fruity Juices scenario (Problem 13.50), formulate and solve a linear optimization model using the auxiliary variable cells method and write a short memo explaining the sensitivity information.

Data from Problem 13.50

Fruity Juices, Inc., produces five different flavors of fruit juice: apple, cherry, pomegranate, orange, and pineapple. Each batch of product requires processing in three departments (blending, straining, and bottling). The relevant data (per 1,000-gallon batch) are shown in the table Data for Problem 50. Formulate and solve a linear program to find the amount of each product to produce.