Joseph Has the Utility Function U(F,H)=10F²H,where F Is the Quantity

Essay

Joseph has the utility function U(F,H)=10F²H,where F is the quantity of food he consumes per year and H is the quantity of housing per week.Suppose the price of food is $10 and the price of housing is $5,while Joseph has an income of $150/week.
a.Calculate Joseph's MRS as a function of the quantities F and H.
b.Write out Joseph's constrained optimization problem with the information provided.
c.Using the substitution method,solve for Joseph's optimal consumption bundle of food and housing.
d.Show that at the optimum,Joseph consumes the bundle along the budget constraint where MRS = MRT.