An aim is what a business is trying to achieve in general terms. An objective is that aim turned into something specific enough to check.
Common aims are survival, profit, growth, market share, customer satisfaction, and the owner's own non-financial goals — independence, or work that fits around a family.
This is the part students lose marks on. A start-up's overriding aim is usually survival — staying solvent long enough to establish itself. Once established, the aim typically shifts to profit and then to growth or market share. A mature business may shift again, to protecting its position or to selling.
So the right answer to 'what should this business aim for' depends entirely on where the business is in its life, and the case study will always tell you.
An objective is useful only if you can tell whether you hit it. The standard test is Specific, Measurable, Achievable, Relevant, Time-bound. 'Grow sales' is an aim. 'Increase sales by 10% by 31 March' is an objective.
If the case study is a start-up, survival almost always outranks profit. Say why, using a fact from the text.