Class 09

Topics

12.1 Deiscrete Random Variables.
12.2 Continuous random variables.
12.3 Expected value and variance.
12.4 Exponential and normal random variables.

Homework questions

12.1: 1,3,5,7,9.
12.2: 1,3,5,7,9,13,15,17,21,23,25,33,35.
12.3: 1,3,5,7,9,11,13,15.

Example questions.

1. A company manufactures 2 products, whose production costs can be described by the equation:

C(x,y) = 77 + 3 x^2 + 2x (y - 11) - 14y + 2y^2.

where x and y denote the output levels of the 2 products (in thousands). A. Find the values of x and y for which the manufacturing cost is minimized, and the cost at this level. Verify that it is a minimum.

B. What is the marginal cost of x if 5 thousand units of x are produced and 3 thousand of y?

C. What is the marginal cost of y if 4 thousand units of y are produced and 3 thousand of x?

D. If twice as much y must be prodcuced as x, use the method of Lagrange Multipliers to identify the minimum cost. Would you expect this cost to be more or less than the cost you found in part a?

Question 2 is OK as it stands! 2. Using the cost function from the previous question, if the manufacturer sells the two products for $10 and $15 respectively, then what values of x and y maximize profits?