Reference no: EM132306858
Chris and Lucy Smith recently purchased a property in Shepparton, Victoria. The property has the capacity to run a variety of grazing and cropping activities. They have hired your services to help them come up with an optimal farm plan.
Activities
The property has 540 hectares of grazing land that is suitable for cattle, wool or lamb production. Both Chris and Lucy have extensive experience in livestock production and are happy to run any of the following activities on their new property.
Your research suggests that the gross margins and resource requirements for the livestock activities are as follows:
| |
Cattle |
Merino |
First - cross lambs |
Prime lambs |
Dorpers |
|
Gross margin ($/hr)
|
720
|
120
|
126
|
118
|
105
|
|
|
|
|
Labour (hr/ha)
|
|
|
|
Spring
|
0.400
|
0.180
|
1.180
|
0.170
|
0.185
|
|
Summer
|
0.350
|
0.125
|
0.125
|
0.120
|
0.110
|
|
Autumn
|
0.370
|
0.120
|
0.120
|
0.115
|
0.085
|
|
Winter
|
0.390
|
0.110
|
0.110
|
0.100
|
0.060
|
|
|
|
|
Feed required (MJ/hd)
|
|
|
|
Spring
|
9,700
|
1,450
|
1,280
|
1,600
|
1,855
|
|
Summer
|
5,850
|
915
|
750
|
865
|
965
|
|
Autumn
|
7,670
|
760
|
790
|
930
|
1,020
|
|
Winter
|
10,120
|
820
|
1,180
|
1,300
|
1,550
|
To intensify their grazing activities, the Smiths have the option of improving the pasture at a cost of $65 per hectare. You assume it will take approximately 1 hour to spread fertiliser across five hectares. The native pasture costs nothing to maintain at low productivity. The feed energy provided by the two types of pasture is as follows:
| |
Feed energy (MJ/ha) |
|
|
Native pasture
|
Improved pasture
|
|
Spring
|
8,370
|
82,800
|
|
Summer
|
6,830
|
14,280
|
|
Autumn
|
6,150
|
9,030
|
|
Winter
|
4,090
|
21,000
|
The property also consists of an additional 300 hectares ideal for growing a variety of crops. The gross margins and labour requirements you have collected for the crop activities are as follows:
|
|
Wheat
|
Barley
|
Triticale
|
Lupins
|
Canola
|
|
Yield (t/ha)
|
2.35
|
2.50
|
2.40
|
1.10
|
1.50
|
|
Price ($/t)
|
330
|
305
|
280
|
350
|
480
|
|
Cost ($/ha)
|
310
|
290
|
270
|
240
|
380
|
|
Spring
|
0.000
|
0.000
|
Labour (hr/ha)
0.000
|
0.000
|
0.000
|
|
Summer
|
2.850
|
2.850
|
2.850
|
0.500
|
0.500
|
|
Autumn
|
0.890
|
0.890
|
0.750
|
1.020
|
1.790
|
|
Winter
|
0.090
|
0.090
|
0.090
|
0.000
|
0.180
|
Constraints
The property consists of two types of land:
• Pasture land (540 ha) covered in native pasture with the potential for improvement.
• Cropland land (300 ha).
Chris can work a total of 450 hours per season (except in summer). Lucy has a part time job in town and can supply only 150 hours or labour per season (except in summer). The Smiths take their annual holiday in summer and can only supply a total of 450 hours of labour during that season.
To maintain soil quality you have suggested that Chris and Lucy implement a rotational constraint of at least one year of lupins for every 2 years of other crops.
Tasks
Using the information you have gathered on the Smith's management preferences and feasible farm activities, design a linear programming model to determine the activity mix that will maximise their profits while satisfying all their constraints.
Answer the following questions.
1. Report the total gross margin, optimal values for each activity and constraint in the base scenario. Report and interpret the shadow prices (200 words).
2. In the base scenario the Smiths produce crops for sale only. Introduce the possibility of feeding barley or triticale to livestock in Autumn. Assume it will take 15 minutes to feed one tonne of these grains. Each tonne of barley contains 12,000 MJ of energy and each tonne of triticale contains 13,000 MJ of energy. Explain your results following the same guidelines as in question 1 (200 words).
3. To alleviate the labour constraint the Smiths would like to explore the possibility of hiring labour at a cost of $40 per hour. Select the seasons they should hire labour based on the results from question 2. Justify your choice. Introduce the option of hiring labour by augmenting the model from question 2. Explain your results following the same guidelines as in question 1 (200 words).
Create tables that summarise the main results of the linear programming and sensitivity analyses. Present these tables in the body of the paper.
Show the full linear programming models and sensitivity analyses from questions 1, 2 and 3 as appendices in your assignment.
Presentation of your Assignment
Reduce your model so that it fits on one page. Change the page size in print preview as described for assignment 1. Cut and paste the relevant section of the summary reports into your assignment to support your arguments. Do not simply include all the reports in an appendix. Be selective in what you present in the body of the report. Present each case and then your discussion on that case in sequential order. Be sure to reference all sources that you use when you provide advice. The marker will assess whether you know how to construct a model and understand how it works, that you can make changes to the model, and interpret the model results. You will need to use supporting evidence for your recommendations.