Mona's preferences for food, F, and clothing, C, are derived by a utility function U(F,C)=FC. Food costs $1 a unit and clothing costs $2 a unit. Mona has $12 to spend on food and clothing.

a. Write the equation for Mona's budget line. If food is on the vertical axis, what is the slope of the budget line?

b. Graph Mona's budget line. Place food on the vertical axis and clothing on the horizontal axis.

c. On the same graph, draw a typical indifference curves that is the utility maximizing indifference curve.

d. Mona is a utility maximizer, write the objective function. Coffee Doughnuts Econ 3070 Prof. Barham 2

e Write down the full optimization problem with the objective function and the constraint.

f. Using calculus and algebra, find the basket of food and clothing that maximizes Mona's utility (i.e. solve the maximization problem you wrote down in

e) (Assume Mona can purchase fractional amounts of both goods