Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

The total cost to manufacture and sell q exactotherms is given by the cost equation C(q) = 2000+5q. The revenue equation is R(q)= 40q - 0.05q^2 dollars for the sale of q exactotherms. Assume the profit is P(q)= R(q) - C (q).   Find the number of items q to sell so that the profit function P(q) has its maximum.    Find on which interval(s) the profit function is increasing and decreasing.

An electronics manufacturer determines that the profit P(in dollars) obtained  by producing and selling x units of a DVD player and y units of a DVD recorder  is approximated by the model P(x,y)=8x+10y-(0.001)(x^2+xy+y^2 )-10,000 Determine the production level that produces maximum profit and also obtain the maximum profit

Determine where y = x4 - 8x2 has a local maximum or a local minimum.

A firm producing two goods "X" and "Y" has the profit function Z = 640X – 20X? + 40XY – 40Y² + 320Y – 140 (a) What are the profit-maximizing level of output for each of the two goods?