Cranberries can be harvested using either a \"wet\" method or \"dry\" method. Dr
ID: 3305359 • Letter: C
Question
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 $33.50 per barrel and wet cranberries are sold for $19.50 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 1,010 hours). Each barrel of dry cranberries requires 0.21 hours in the dechaffing operation and 0.34 hours in the cleaning operation. Wet cranberries require 0.07 hours in the dechaffing operation and 0.10 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 0.26 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.
Let W = barrels of cranberries harvested using wet method
Let D = barrels of cranberries harvested using dry method
__________D
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. Round your answer for Total Cost to the nearest cent.
Optimal solution : W- ?? D-??
Total cost = ??
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/should not)____ purchase additional dechaffing capacity.
Why or why not?
The dechaffing (Constratint 2) ____(is/ is not)___ a binding constraint because only _____ of the 1,010 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 1,010 available hours increases (decreases) revenues $______ based on the Dual Values shown here. This is true for any cleaning capacity value between _______ and __________.
__________D
s.t. __________W + __________D ___________ Total Harvest __________W + __________D ___________ Dechaffing __________W + __________D ___________ Cleaning __________W + __________D ___________ Drying W, D 0Explanation / Answer
a)'
Price of wet cranberry barrel is 19.5 and that of dry cranberry is 33.5 and hence the total price can be give by the equation
MAXIMISE 19.5 * W + 33.5 * D
s.t
1 * W + 1 * D <=4000 (Total number of barrels of cranberry including wet and dry split is 4,000)
0.07 * W + 0.21 * D <= 1010 (Total number of dechaffing hours is 1,010 and Wet barrel requires 0.07 hours and dry barrel requires 0.21 hours)
0.1 * W + 0.34 * D <= 1010 (Total number of clearning hours is 1,010 and Wet barrel requires 0.1 hours and dry barrel requires 0.34 hours)
0.26 * W <= 1010 (only wet barrel cranberries are dried and they require 0.26 hours)
b) Solving this using solver in excel
We get
W as 1459, D as 2541
total cost or price is $ 113,574
c)
Fresh Made (should/should not) should not purchase additional dechaffing capacity.
Why or why not?
The dechaffing (Constratint 2) (is/ is not) is not a binding constraint because only 636 of the 1,010 available hours are being used.
d)
Assuming everything else remains unchanged, each additional hour of cleaning capacity (Constraint 3) added (subtracted) from the 1,010 available hours increases (decreases) revenues to $ 134,000 based on the Dual Values shown here. This is true for any cleaning capacity value between 1010 and 1360
Beyond 1360 hours (4000*0.34) of cleaning the dry barrels don't go beyond 4,000.