4. Claudia has the following preferences over two goods, c and d: U(c, d) = min{c/2, 3d) Let pc = 2 and pd=3. a. What combination of c and d will give Claudia exactly 18 units of utility at the lowest possible cost? b. How much will this bundle cost? c. If the price of c rises to 3 and the price of d stays the same, will the expenditure minimizing bundle change? Why or why not? d. Solve for Claudia’s Hicksian demand functions for c and d. e. Write down Claudia’s expenditure function E(pc, pd , U). f. Using Shephard’s Lemma, derive Claudia’s Hicksian demand function for d.