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John and Max need to purchase two common fertilizers which will be combined to produce a new fertilizer (if a secret ingredient is also added). The cost per kilogram of each fertilizer and their trace element percentages are given in the following table.
Fertilizer
Cost ($) per kg
% nitrogen
% potassium
A
6
4
10
B
7
3
To ensure success John estimates the percentage of Potassium in the final mix should be between 4% and 9% of the total mass, but does not think the percentage of Nitrogen is important in the outcome. To allow for a number of trials John and Max want to produce as much of this new fertiliser as they can. However they only have $53 as the total budget for purchasing both fertilisers.
Note: You can ignore the mass of the secret ingredient in your calculations.
(a) How much of each fertilizer should John and Max buy to maximise the amount of fertilizer made in order to meet these constraints.
(b) Max thinks that the percentage of Nitrogen is also important and should be between 5% and 9% in addition to John's Potassium constraint. How much should you buy given Max's advice?
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