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 4000 barrels of cranberries that can be harvested using either the wet or dry method. Dry cranberries are sold for $28.50 per barrel and wet cranberries are sold for $14.50 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 seasons about 6 weeks long (for a total of 1,008 hours). Each barrel of dry cranberries requires 0.16 hours in the dechaffing operation and 0.28 hours in the cleaning operation. Wet cranberries require 0.02 hours in the dechaffing operation and 0.08 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 0.21 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 there is a + sign before the blank. Enter "O" if your answer is zero. If the constant is "1" it must be entered in the box. Let W = barrels of cranberries harvested using wet method Let D = barrels of cranberries harvested using dry method 14.5 W + 28.5 VD Max s.t. Total Harvest 1 VW+ 0.02 + 0.08 x W + 0.21 w + 1 VDS 4,000 0.16 VDS 1,008 0.28 VDS 1,008 0 VDSL 1,008 W, D 20 Dechaffing Cleaning Drying b. Solve a linear program in part (a). How many barrels should be dry harvested? How many barrels should be wet harvested? Round your answers to two decimal places. b. Solve a linear program in part (a). How many barrels should be dry harvested? How many barrels should be wet harvested? Round your answers to two decimal places. Optimal Solution: W 3,787.34 x 212.66 x c. Suppose that Fresh Made can increase its dechaffing capacity by using an outside firm for this operation. Fresh Made will still use its own dechaffing operation as much as possible, but it can purchase additional capacity from this outside firm for $500 per hour. Should Fresh Made purchase additional dechaffing capacity? If required, round your answer to three decimal places. Fresh Made should not purchase additional dechaffing capacity. Why or why not? The dechaffing (Constraint 2) is not a binding constraint because only 109.772 X of the 1,008 available hours are being used. d. Interpret the dual value for the constraint corresponding to the cleaning operation. How would you explain the meaning of this dual value to management? If required, round your answers to two decimal places. Assuming everything else remains unchanged, each additional hour of cleaning capacity (Constraint 3) added (subtracted) from the 1,008 available hours increases (decreases) revenues $ X based on the Dual Values shown here. This is true for any cleaning capacity value between x and X