1 If two products A and B have demand functions that depend on each other, 9, = 100 - 5pa+ PAPB = 250 - 10 In(pg+ 1) + will they be competitive, complementary, or neither. Show the relevant calculations. and PA+PB

Suppose that a demand function is given by q = D(p) = 20(7 - ((p) with superscript (2)/square root of ((p) with superscript (3) + 1))) , where q is the demand for a product and p is the price per unit in dollars. Find the rate of change in the demand for the product per unit change in price. a.(dq/dp) = (-20(p) with superscript (4) + 80p/(((p) with superscript (3) + 1)) with superscript (1/2)) b.(dq/dp) = (10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (3/2) ) c.(dq/dp) = (-10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (1/2) ) d.(dq/dp) = (-10(p) with superscript (4) - 40p/ (((p) with superscript (3) + 1)) with superscript (3/2) )

A firm has the following total-cost and demand functions:     C = 1/3^Q3 - 7Q2 + 111Q + 50                  Q = 100 - P Write out the total-revenue function R in terms of Q Formulate the total-profit function π in terms of Q F ind the profit-maximizing level of output Q* What is maximum profit?

7. Find the price per unit p that produces the maximum profit given C 2500-75x +0.04x? ar p%3D2000-0.6x? Use P xp-C