Consider the utility function; u (x1, x2) = (x1 - 2) (x2 - 3)with accompanying budget constraint p1x1 + p2x2 = I. [a] Write down the optimality conditions for maximizing the utility function subject to the budget constraint.[b] Derive the demand functions x1* (p1,p2,I) and x2* (p1,p2,I).[c] Find the own price elasticity of demand and the income elasticity of demand for good 1.[d] Are goods x1 and x2 substitutes or complements? Also, does consumption of x1 increase or decrease in income? Using the appropriate derivatives to answer these questions.[e] State the general form of the Slutsky equation for good 1 (denote the compensated demand for good 1 as x1c (p1; p2; U par) without solving for the expenture minimization find the slope of the compensated demand function for good 1 with respect to p1 (this constitutes the substitution effect and can be obtained from the Slutsky equation and your answers in [b]).