Citrus Delight is a producer and processor of frozen orange juice concentrate. They sell two brands of orange juice concentrate - regular quality and super high quality, that are made from all or some of four processes called process A, process B, process C, and process D.

Relevant data are given below:

 

For example, process B uses 5 pounds of normal oranges and 2 pounds of very good oranges to make 5.5 pounds of regular quality concentrate and 1.5 pounds of waste product. The regular quality orange concentrate sells for $10.00 per pound and the super high quality orange juice sells for $14.00 per pound. This month Citrus has contracted to buy 19,000 pounds of normal oranges and 14,000 pounds of very good oranges. They want to know which processes to use and at which levels, in order to maximize revenue. The LP formulation and its output for this problem are:

 

(a) According to the given LP formulation, what are the definitions for decision variables A, B, C, and D, respectively? Be sure to include the right units in your definitions.

(b) Why is the objective function coefficient for process B equal to 55?

(c) What is the amount of super high-quality frozen concentrate that is produced?

(d) What is the total revenue? (be sure to use the right units!)

(e) How much should Citrus Delight be willing to pay for additional normal oranges? 5

(f) The purchasing department is able to acquire additional 10,000 pounds of normal oranges, what will be the new optimal revenue?

(g) The engineering department has concluded that by retrofitting, they can reduce the wastage in process A from 1 pound to .4 pounds, increasing the yield of regular quality concentrate from 6 to 6.6. Should this change be considered? Why or why not?

Process D Inputs normal oranges (pounds) very good oranges (pounds) Outputs regular quality concentrate (pounds) super high quality concentrate (pounds) waste (pounds) 4 3 4 7 6. 5.5 9. 1 1.5 1 3