# optimisation (part a): the method ## aim turn the words into one function of \(x\), then optimise --- # step 1 — find the cold, hard fact what is fixed in the question? examples - total length of wire - total fencing - total material - total cost write this as an equation --- # step 2 — choose variables let - \(x=\dots\) - \(y=\dots\) (always include units in words) --- # step 3 — write the equation linking \(x\) and \(y\) this comes from the fixed information example \[ 2x+2y=40 \] --- # step 4 — make \(y\) the subject rearrange to get \[ y=\dots \] --- # step 5 — decide what they want to optimise usually - area - volume - surface area - cost call it \(A, V, S,\) or \(C\) --- # step 6 — write it in terms of \(x\) and \(y\) before substituting example \[ A=xy \] --- # step 7 — substitute for \(y\) now you have \[ A(x) \] a function of one variable --- # step 8 — optimise differentiate, set to zero, and use a nature table --- # step 9 — conclude state the answer clearly in words, with units