An icecream lover has a total of $10 to spend one evening. The price of icecream is $p per litre. The person's preferences for buying q litres of icecream, leaving a nonnegative amount $(10 pq) to spend on other items, are represented by the utility function: U(q)=\\/+2\\/10p, (16 [0,13]. (a) Find the rstorder condition for a utility maximizing quantity of icecream. [Hint the square root function is a power function with exponent %.] (b) Solve the rstorder condition derived in (a) in order to express the utility maximizing quan tity (1* as a function of p. (c) What guarantees that your quantity q* is really a maximum? (d) Express the elasticity of demand for icecream as a function of the price 35;) per litre. When the price is $2.50 per litre, calculate the price elasticity of the person's demand for icecream