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 5500 barrels of cranberries that can be harvested using either the wet or dry method. Dry cranberries are sold for $36.50 per barrel and wet cranberries are sold for $22.50 per barrel. Once harvested, cranberries must go through dechaffing and deaning 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 0.32 hours in the deaning operation. Wet cranberries require o.05 hours in the dechaffing operation and O.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 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. Max 22.50 36.50 D 5,500V Total 1,008Dechaffing 0.05 W+ 0.16 D 0.11 w0.32 D 1,008 Cleaning 0.23 W+ OD1.,008Drying 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. 1,008 Drying should be wet harvested? Round your answers to many two decimal places. W 3,542.86 X D 1,957.14 X e 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. purchase additional dechaffirp capacty. Fresh Made should not Why or why not? Constrant 2 is not a binding constraint because only The dechaffing X of the 1,008 available hours are being used. 815 d. Interpret the dual value for the constraint corresponding to the cleaning operation. How would you explain the meaning of this dual value to Assuming everything else remains unchanged, each additional hour of deaning capacity (Constraint 3) added (subtracted) from the 1,008 available based on the Dual Values shown here. This is true for any dleaning capacity value between (decreases) revenues $ hours and Partially correct

Answer 1

Solver screenshot

Obiective function 150616.7 3580.952 1919.048 4 Total Harvest 5500 <= 5500 5 Dechaffing 0.05 0.16 486.0952 1008 6 Cleaning 0.11 0.32 1008 1008 7 Drying 0.23 0 823.619仁 1008

Sensitivity report

A B 1 Microsoft Excel 16.0 Sensitivity Report 2 Worksheet: [Book1]Sheet11 3 Report Created: 29-05-2019 10:34:37 4 6 Variable Cells Final Reduced Objective Allowable Allowable Value Coefficient Increase Cell Name Cost Decrease 9 $B$3 W 3580.952381 0 22.5 14 9.953125 10 $C$3 D 1919.047619 0 36.5 28.95454545 14 12 Constraints Final Shadow Constraint Allowable Allowable 13 Price 14 Cell Value R.H. Side Increase Decrease Name 15 $DS4 Total Harvest 5500 15.16666667 5500 526.0869565 2350 16 $D$5 Dechaffing 486.0952381 0 1008 1E+30 521.9047619 17 $D$6 Cleaning 18 SD$7 Drying 1008 66.66666667 1008 752 168.3478261 823.6190476 0 1008 1E+30 184.3809524 19

b)

Barrels of dry harvested = 1919.05

Barrels of dry harvested = 3580.95

c)

Fresh Made Should not purchase additional dechaffing capacity

The dechaffing capacity is not a binding constraint because only 486.09 of the 1008 hours are being used

d)

Assuming everything else remain unchanged, each additional hour of cleaning capacity (constraint 3) added (subtracted) from the 1008 available hours increases (decreases) revenues $ 66.67 based on the dual values shown here, This is true for any cleaning capacity value between 839.65 and 1760