3. The utility that Aisha receives by consuming food F and clothing C is given by U(F, C) = FC + F + 2C. Food costs 1 a unit, and clothing costs 2 a unit. Aisha's income is 21. MUF = C+1 and MUC = F+2.

(i) Define the term Marginal Rate of Substitution (MRS). (3 marks)

(ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (5 marks)

(iii) Now suppose that price of C and Aisha's income remain unchanged at 2 a unit and 21 respectively while price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF). (7 marks)