Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is
the profit in dollars when x hundred unit of item A and y hundred
units of item B are produced and sold.
A.Find how many items of each type should be produced to
maximize profit?
B.Use the Second Derivates Test for local extrema to show that
this number of items A and B results in a maximum?
Questions 11-13 relate to the following consumer utility
maximization problem: maximize U(x,y)=x^0.75y^.25 subject to the
budget constraint 10x+5y=40.
A) What is the optimal amount of x in the consumer's bundle?
(Note that the 10 in the budget constraint is interpreted as the
price of good x, 5 is the price of good y, and 40
is the consumer's income.)
B) What is the optimal amount of y in the consumer's bundle?
C) What is the consumer's maximized utility?