Essay About Shadow Prices And Optimal Plan

Inventory Models
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QM 265
Assignment 6
Inventory Models
Table of Contents
Base case linear programming model
Page 3
Optimal plan and corresponding total gross margin
Page 4
Constraints for scenarios with final values and shadow prices
Page 5
Shadow prices for cattle and summer casual labour
Page 5-6
Changes in the optimal plan between scenarios A and C
Page 6
Binding and upper and lower limits on resources
Page 6-7
References
Page 8
Question 2) a)
Table 1. Optimal plan and corresponding total gross margin.
Activity
Gross Margin Change (Plan B)
Forage Oats (ha)
Improved Pasture (ha)
55.87
Native Pasture (ha)
Fallow (ha)
Merino Ewes (hd)
Xbred Ewes (hd)
910.88
Cattle (hd)
Spring Supplementary Feed (kg)
Summer Supplementary Feed (kg)
Autumn Supplementary Feed (kg)
Winter Supplementary Feed (kg)
Spring Casual Labour (hrs)
Summer Casual Labour (hrs)
Autumn Casual Labour (hrs)
Winter Casual Labour (hrs)
99.96
Total Gross Margin
80221.48
Table 2. Constraints for the three scenarios with final values and shadow prices.
Constraints
Base Case
Labour Change
GM Change
Final Values
Shadow Prices
Final Value
Shadow Price
Final Value
Shadow Price
Merino Ewes (minimum)
-400.00
24.49
-400.00
14.49
-400.00
24.49
Xbred Ewes (minimum)
-910.88
-910.88
-912.57
Cattle (minimum)
-20.00
411.97
-20.00
411.97
-20.00
412.78
Total Sheep (maximum)
1310.88
1310.88
1312.57
Arable (ha)
Fallen Timber (ha)
150.00
150.00
37.43
Crop Rotation (ha)
Spring Labour (hrs)
220.00
180.65
220.00
180.65
220.00
259.33
Summer Labour (hrs)
220.00
101.56
220.00
101.56
220.00
23.26
Autumn Labour (hrs)
151.18
151.18
147.45
Winter Labour (hrs)
180.00
17.00
180.00
17.00
180.00
17.00
Spring Feed (kg/ha)
-151016.12
-151044.06
-131942.93
Summer Feed (kg/ha)
-134868.66
-134857.49
-114012.79
Autumn Feed (kg/ha)
Winter Feed (kg/ha)
-17335.15
-17363.09
Spring Grain (t)
Summer Grain (t)
Autumn Grain (t)
Winter Grain (t)
Spring Casual Labour (hrs)
115.00
163.65
115.00
163.65
115.00
242.33
Summer Casual Labour (hrs)
115.00
84.56
115.00
84.56
115.00
Autumn Casual Labour (hrs)
Winter Casual Labour (hrs)
66.96
66.96
67.26
Non Arable (ha)
55.87
55.87
137.75
Total Gross Margin
76221.48
80221.48
75765.69
The shadow price of a resource, such as labour or hectares, is the effect an increase or decrease of one unit of a resource has on total gross margin (TGM). Therefore it