Fertiliser Calculator

For those in the agricultural community this application is intended to simplify the task of working out how many bags of fertiliser containing certain N:P:K percentages to buy when the spread rate for applying a top dressing is known.
The application will also attempt to calculate an optimised number of bags to use by varying the spread rate values slightly. If a smaller number of bags can be found then the optimised number of bags will be displayed along with the spread rates to use.
Optionally a cost per bag value can be entered and the program will then display the total cost of the bags required and the optimised number of bags.
It is also useful to quickly calculate whether using bags of fertiliser with different N:P:K percentages would use fewer bags and which could possibly be a cheaper alternative.

You enter:
The percentages of the N, P and K contained in a single bag of fertiliser, the N:P:K value for the fertiliser.
The weight of a single bag of fertiliser and optionally the cost of a single bag.
The required weights (or spread rates) of each type (N, P or K) over a unit area of land.
The area of the land to be treated

The program will:
Calculate and display the minimum number of bags of fertiliser required and optionally the cost if you entered the cost per bag.
Display an optimised number of bags of fertiliser required, if one exists. The cost of the optimised number of bags will be displayed if a cost per bag value was entered.
Display optimised spread rates, if they exist.
The optimised number of bags required calculation is achieved by the program making small adjustments to the user supplied spread rates. If any combination is found that results in less bags of fertiliser being required then this value is displayed as the optimised number of bags and spread rates.