I have a question relating to the following problem in my maths investigation:
A nut store orders nuts in bulk, and the mix ratios are as follows:
Budget Mix: 60% peanuts, 40% cashews Entertainers MiX: 40% peanuts, 40% cashews and 20% macadamias Premium Mix: 30% peanuts, 30% cashews and 40% macadamias
This can be represented as a matrix:
Peanuts 0.6 0.4 0.3 Cashews 0.4 0.4 0.3 Macadamias 0 0.2 0.4
One week, they are given an order of 1360kg of peanuts, 1260kg of cashews and 2000kg of macadamias. How many packs of each type of mix could be made if they aimed to use all of the nuts supplied? Or by minimising the number of nuts left over.
To use all nuts, they would make 500 packs Budget, -1760 packs Entertainers and 5880 packs of Premium. This is impossible however, as you obviously cannot make -1760 packs.
How would I go about finding the least amount left over? Is there a technique or formula I could use? Or is trial and error the only option?
Thanks in advance!! :)