Schoolboy Charlie loved his snack treats, especially sweets and chips. His parents gave him $50 per month pocket money that he could spend on healthy canteen options, but Charlie had other plans for the money. He modelled a Satisfaction Index function that he planned to maximise based on the number of servings of his favourite snacks as follows: SI = VS + 210 where S was the number of sweet servings per month (which may be not a whole number) and C was the number of servings of chips (Charlie slightly preferred the chips). The price per serving of sweets was $5.00 (per packet) and chips cost $2.00 per serving. 

(a) Formulate the Lagrange Function based on this information.

(b) Using the method of Lagrange Multipliers, find the combination of sweets and chips servings to maximise Charlie's Satisfaction Index function (SI) restricted by his pocket money budget.

(c) Estimate the increase in his Satisfaction Index function if his parents were to give him an extra dollar to spend each month and relate your findings to the value of the Lagrange multiplier.