It is known that a typical Utopian citizen consumes only two goods: tobacco and food.

Extensive time-series research on the Utopian consumer has yielded the following utility function:

U(x1, x2) = x1

x2,

Where:

x1 denotes the monthly consumption of tobacco

x2 denotes the monthly consumption of food

unit prices of these goods are $2 for x1 and $4 x2

the total monthly expenditure on these goods is $300.

(a) Show that if the budgetary constraint is satisfied, the maximum value of U is 500 and state the

corresponding values of x1 and x2.

(b) Verify that the stationary point is a maximum.