Show full answers to part d) e) & f) Caroline is a consumer who enjoys candys. Her preferred are licoricecandies (good x) and sour candies (goody y), as given by the utility function u(x, y) = xy. Todayis Sunday and she is visiting a store where the per unit price of licorice candies is px = $1 and theper unit price of sour candies is py = $2. Today she is willing to spend $12 on candies.a) Using appropriate scale, draw Caroline's indifferences curves representing utilitylevels U = 6 and U = 12. Label these indifference curves as U6 and U₁2, respectively.b) Write the equation of Caroline's budget line and draw it on the same graph as in (a).c) Look at your graph, can Caroline afford any bundle of candies that gives her utility ofU = 6? What about utility of U = 12? Explain.d) If we want to model Caroline's optimal candy-choice problem as a utility maximizationproblem (UMP):●What would be the objective function and the constraint of this problem?Formally (with notation) write the statement of her optimal choice problem.Conceptually (in words), rewrite the statement of her optimal choice problem.[Hint: Review notes/slides/exercise from D01 to see how we describe and writeoptimization problems]e) Mathematically, solve Caroline's UPM to find her optimal candy-bundle today.f) What is level of utility Caroline gets from consuming her optimal bundle found in part(e)?

The Utility function is defined for graphing the indifference curves.Indifference curve represents…

d) If we want to model Caroline's optimal candy-choice problem as a utility maximization problem (UMP): ● What would be the objective function and the constraint of this problem? ● Formally (with notation) write the statement of her optimal choice problem. Conceptually (in words), rewrite the statement of her optimal choice problem. [Hint: Review notes/slides/exercise from D01 to see how we describe and write optimization problems] e) Mathematically, solve Caroline's UPM to find her optimal candy-bundle today. f) What is level of utility Caroline gets from consuming her optimal bundle found in part (e)? ●