MGOC10H3 Lecture Notes - Lecture 9: Contin, Unita, Nissan Sd Engine

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MGOC10 - Business Report
Problem 2
Ramesha Javed
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Ramesha Javed
Executive Summary
Problem 2
The issue at hand was to determine the optimal amount of dry and wet cranberries to harvest
through the development of a linear programming model. A brief summary of the key findings
are noted below.
The most important factors that affect the revenue of the company with regards to dry and wet
barrels of cranberries harvesting are the total number of cranberries that are to be harvested,
the price of the cranberries being sold, the total number of hours for dechaffing and cleaning
operations, and the number of hours that can be used for dechaffing and cleaning of wet
cranberries and dry cranberries.
In order to maximize revenue, the model indicates that the optimal amount to harvest would be
2309 dry barrels and 2690 wet barrels of cranberries. A total of 523.27 hours are being used for
dechaffing operations from a capacity of 1008 for dry cranberries. A total of 592 hours out of
1008 hours are being used for drying operations for dry cranberries and a total of 1008 hours
out of 1008 hours are being used for cleaning operations for dry cranberries. The cleaning hours
are being used at capacity. Lastly, according to the model, revenue is being maximized at $
122,136.36.
Please see below for further information regarding the details of our findings through the linear
programming model.
a) Let WC = the number of wet cranberries that are manufactured
Let DC = the number of dry cranberries that are manufactured
Objective function:
Maximize Revenue – 17.5*WC + 32.5*DC
Constraints:
2
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Ramesha Javed
WC + DC <= 5000
0.04WC + 0.18DC <= 1008
0.1WC + 0.32DC <= 1008
o.22WC <= 1008
All variables >= 0
b) Approximately 2309 dry barrels and 2690 wet barrels of cranberries should be harvested to
maximize revenue. (Appendix 1)
c) Fresh Made should not purchase additional capacity because the total hours being used for
dechaffing are approximately 523.27 from a capacity of 1008 hours. This indicates that there are
484.74 slack hours left for dechaffing operations. Therefore, there is no need to purchase the
additional capacity as the capacity is not being exhausted currently in order to maximize revenue.
(Appendix 2)
d) Based on the excel output, the dual value is 68.18 and the corresponding range of feasibility is
between 1600 and 592 (1008 + 592, 1008 – 416). This can be interpreted as meaning that within
the feasible range, if the cleaning hours for dry cranberries are increased by 1 unit, the revenue will
go up by 68.18 and if the hours are decreased by 1 unit, the revenue will drop by 68.18. However, if
the hours are changed beyond the feasible range, we are not sure if the dual value is still applicable
in terms of the increase or decrease in revenue by 68.18 as a result of change in one unit in the
hours. (Appendix 2,3)
3
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