""'' ' \\ ___'_"I An ice-cream lover has a total of $30 to spend one evening. The price of ice-cream is $19 per litre. The person's preferences for buying 6] litres of ice-cream, leaving a nonnegative amount $(30 pq) to spend on other items, are represented by the utility function: 30 0, . U(q)=\\/+\\/30pq, qe p (a) Find the rst-order condition for a utility maximizing quantity of ice-cream. [Hintz the square root function is a power function with exponent 1/2.] (b) Solve the rst-order condition derived in (a) in order to express the utility maximizing quantity of as a function of p. (c) What guarantees that your quantity (1* is really a maximum? ((1) Express the elasticity of demand for ice-cream as a function of the price $ p per litre. When the price is $3 per litre, calculate the price elasticity of the person's demand for ice-cream