Question
Linear Programming
Complete the linear programming matrix at the end of the question with the appropriate coefficients and signs for the following information
Labour
|
Requirements steers ewes lambs oats turnips barleys millet
|
|
Winter (hrs) 1.22 0.20 0.12 0.30 0.10 1.00 0.70
Spring (hrs) 1.20 0.30 0.15 0.20 0.30 0.80 1.10
Summer (hrs) 1.12 0.20 0.13 0.30 1.30 1.30 1.50
Autumn (hrs) 1.14 0.40 0.30 0.20 0.20 0.20
|
|
Feed demand steers ewes lambs
|
|
Winter (kg) 900 192 36
Spring (kg) 800 190 57
Summer (kg) 830 190 95
Autumn (kg) 790 200
|
|
Feed supply oats turnips barley millet
|
|
Winter (kg) 840 110 460
Spring (kg) 280 580 500
Summer (kg) 675 175 2700
Autumn (kg) 470 163
|
|
Gross margins steers ewes lambs oats turnips barley millet
|
|
$ 74.05 23.20 54.32 -43.45 -48.36 -39.60 -36.74
|
The manager has 800 hours of family labour available in summer, autumn and winter; however, in spring only 750 hours is available. In the district casual labour is worth $14 per hour.
Tasks
1.Fill in the tableau with the values from the above information: be sure to include the correct signs, gross margins and supply values. You are not required to complete a demand column.
2.Complete the constraints for a 2-year crop rotation between oats and barley in the homestead paddock (300 ha).
3.Complete the constraint for turnip and millet production in the South Hill paddock (200ha).
4.Complete the constraint for a maximum of 40 steers.
5.Complete the constraint for a 75 per cent lambing ratio.
6.Complete the constraint for a minimum 200 head of sheep.
7.Show how a maximum of 5 tonnes of feed wheat could be made available in winter at $160 per tonne.