How should management go about deciding what part of its budget it should allocate to ensure good customer care/relations?

One of the golden questions I ever come across!

This question should be thrown to every Head of the Organisation to think a lot on this. 

Very straight forward ! 10% of the net profit should be budget allocated to this area. No mean and lean approach on this. we must be generous towards to the customers who are primarily the reason for profit, next to employees.

Viewing embedded disposition of the client and determine walk carefully about what is practical and hale

Know the annual profit of the organisation & allocate the part of it to improvement on Quality with SPC(VOC) & Delivery with time(VOC), reduction in wastage.

The short answer is understanding the Customer need first. In general the principle of Highest Common Denominator principle is used for designing a program , but does not meet most of needs of the end customer. Hence to me the important aspect of customer service is understanding the customer needs & expectations.

 

All expenditure should be viewed as an investment and management should consider how to get the best return on the total investment. Delivering good service means giving the people who really matter (the front line) the resources that they need i.e. training, equipment, systems, support and leadership.

This is dangerous.  You should not decide what budget to decide to a particular area.  You should decide what you want to achieve in all areas, figure out how much it will all cost, and go from there. 

Allocating budget in the manner described in the question is guaranteed to result in misallocation of resources.