linear programming 5
henderson farm Llama and kunekune
Henderson Farm breed llama and kunekune (pigs) on their farm. Llama require 2 hours of labour for each animal and kunekune require 1 hour of labour for each animal. There are 900 hours of labour available.
There are 1200 hectares of land available on the farm. 1 hectare of land can support 1 llama or 3 kunekune (L + 3K = 1200)
To break even, the farm needs to breed at least 50 llama and at least 50 kunekune.
The current price for an average kunekune is $100 and a llama is $400. This gives an income equation of
I = 400L + 100K
How many of each animal should they farm to maximise profit?
If the income changes to a 2:1 ratio how does this affect their options for maximisation?
There are 1200 hectares of land available on the farm. 1 hectare of land can support 1 llama or 3 kunekune (L + 3K = 1200)
To break even, the farm needs to breed at least 50 llama and at least 50 kunekune.
The current price for an average kunekune is $100 and a llama is $400. This gives an income equation of
I = 400L + 100K
How many of each animal should they farm to maximise profit?
If the income changes to a 2:1 ratio how does this affect their options for maximisation?
I = 400L + 100K
A(50,383) = $58300
B(300,300)=$150000
C(425,50)=$175000
D(50,50)=$25000
Henderson Farm need to allocate 425 llama and 50 kunekune to make a max income of $175000
A(50,383) = $58300
B(300,300)=$150000
C(425,50)=$175000
D(50,50)=$25000
Henderson Farm need to allocate 425 llama and 50 kunekune to make a max income of $175000
using the ratio 2:1
A possible solution to the ratio problem is
I = 200L + 100K
A(50,383.33) = $48333 (using the full decimal answer to avoid rounding error)
B(300,300)=$90000
C(425,50)=$90000
D(50,50)=$15000
Using points B and C, to maximise their income under a ratio of 2:1 they should allocate 300 llama and 300 kunekune OR 425 llama and 50 kunekune.
The two points B and C lie on the line 2L + K = 900 and rearranging gives
L = -1/2 K + 450
Here the gradient = -1/2
The new income equation also has the same gradient:
200L + 100K = 90000
L = -1/2K + 45
This means the graph of the equation for the new income runs parallel to the boundary line that the points B and C are on.
I = 200L + 100K
A(50,383.33) = $48333 (using the full decimal answer to avoid rounding error)
B(300,300)=$90000
C(425,50)=$90000
D(50,50)=$15000
Using points B and C, to maximise their income under a ratio of 2:1 they should allocate 300 llama and 300 kunekune OR 425 llama and 50 kunekune.
The two points B and C lie on the line 2L + K = 900 and rearranging gives
L = -1/2 K + 450
Here the gradient = -1/2
The new income equation also has the same gradient:
200L + 100K = 90000
L = -1/2K + 45
This means the graph of the equation for the new income runs parallel to the boundary line that the points B and C are on.