Problem 3-27 (Algorithmic) Cranberries can be harvested using either a \"wet\" m

Question

Problem 3-27 (Algorithmic) Cranberries can be harvested using either a "wet" method or "dry" method. Dry-harvested cranberries can be sold at a premium, while wet harvested cranberries are used mainly for cranberry juice and bring in less revenue. Fresh Made Cranberry Cooperative must decide how much of its cranberry crop should be harvested wet and how much should be dry harvested. Fresh Made has 5000 barrels of cranberries that can be harvested using either the wet or dry method. Dry cranberries are sold for $30.50 per barrel and wet cranberries are sold for $16.50 per barrel. Once harvested, cranberries must go through dechaffing and cleaning operations. The dechaffing and the cleaning operations can each be run 24 hours per day for the 6-week seasons (for a total of 1,014 hours). Each barrel of dry cranberries requires 0.18 hours in the dechaffing operation and 0.30 hours in the cleaning operation. Wet cranberries require 0.05 hours in the dechaffing operation and 0.11 hours in the cleaning operation. Wet cranberries must also go through a dry process. The drying process can also be operated 24 hours per day for the 6-week season, and each barrel of wet cranberries must be dried for 0.23 hours. a. Develop a linear program that Fresh Made can use to determine the optimal amount of cranberries to dry harvest and wet harvest. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if thereis sign before the blank. Let W- barrels of cranberries harvested using wet method Let D barrels of cranberries harvested using dry method Max Total Harvest Dechaffing Cleaning Drying W, D20

Explanation / Answer

a)

The objective function maximizes the total revenue generated from wet-harvested cranberries and dry-harvested cranberries. Each barrel of wet-harvested cranberries generates $16.50 in revenue; dry-cranberries earn $30.50 per barrel. The first constraint ensures that no more than 5,000 total barrels of cranberries are harvested. The second constraint states that every barrel of wet-harvested cranberries requires 0.04 hours in the Dechaffing operation, every barrel of dry-harvested cranberries requires 0.18 hours in the Dechaffing operation, and there are 1014 Dechaffing hours available. The third and fourth constraints represent similar requirements for the cleaning and drying operation

Let W = barrels of cranberries harvested using wet method

Let D = barrels of cranberries harvested using dry method

Max   16.5 W+30.5 D

W+D 5,000 Total Harvest

0.04 W+0.18 D 1,014 Dechaffing

0.11 W+0.30 D 1,014 cleaning

0.23 W 1,014 drying

W, D 0 No negativity

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