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# D1 Maths - Linear Programming Help watch

1. Hi can anyone help me with this question?

- A horticulturist needs to fertilise a plot ready for sowing a crop in the spring. Two fertilisers are available, 'supergrow' and 'plus'. A bag of supergrow provides 3kg nitrogen and 4kg of phosphate. a bag of plus provides 4kg of nitrogen and 2kg of phosphate. The horticulturist requires at least 24kg of nitrogen and at least 22kg of phosphate. A bag of supergrow costs £5 and a bag of plus costs £4. The horticulturist wishes to determine how many bags of each fertiliser he needs to purchase in order to keep the cost of growing his crop to a minimum.

a)Formulare this as a linear programming problem
b)Solve this linear programming problem graphically using the ruler method to find the optimal solution

I think i can do part B but I'm having trouble formulating it

Any help would be appreciated!
2. As far as I'm aware to get the marks in the exam you just have to plot one objective line and then you can just state the vertex where the cost is minimised, and then plug those values back into initial equation
3. list all key points in the question so then you can start thinking of some inequalities
so if n=1kg of nitrogen and p=1kg of phosphate
24≤n
22≤p
if S=number of supergrow bags, S=3n+4p
if N=number of plus bags, N=4n-2p

the objective line would be 5S+4N, and then that is equal to 5(3n+4p)+4(4n-2p) and you can expand that and make it equal to the cost(C)

idk if this is the right way just giving a different angle linear programming is my least favourite because I hate graphs but I hope I helped a little

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Updated: February 8, 2016
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