Dana is a wheat farmer. She has three fields which she has harvested and stored in three separate grain bins.

Each field has different characteristics and hence the quality of the wheat stored in each bin is different.

She wants to maximise her profit by blending wheat from the bins to maximise the amount of High Protein

Grade wheat she has to sell

High Protein grade wheat needs to meet two criteria:

$$ minimum $14\%$ protein by weight

$$ maximum $12\mathrm{.}5\%$ moisture by weight

You task is to determine how Dana should blend the wheat from her three bins to maximise the amount of High Protein grade wheat she can sell.

In order to deal with numerical precision problems $($because floating point numbers are not exact$),$ all test cases will accept an error of up to $0\mathrm{.}01$ tonnes.

Hint: You can solve this in two steps by first determining the amount of wheat from each bin required to make exactly $1$ tonne of High protein grade wheat with the correct percentages for protein and moisture.

This is a system of $3$ equations with $3$ unknowns. The second step is to scale this so that you run out of wheat in one bin.