Lecture: wrap up 4.2 (linear programming), then 5.1 (exponential functions)

Office hours: 1:30-2 in CDH 109 (+ TUESDAY 10-11 in PDL C-326, and 2:30-3:30 in MSC)

Quiz Section Tomorrow: Hwk Q&A + Test Prep

HOMEWORK Section 4.2 is due Tuesday night. (section 5.1 on Thursday, and 5.2 on Friday night)

Why was the math book sad? -

(Vennebush, Patrick. "Math Jokes 4 Mathy Folks ")Because it had so many problems.-

AnnouncementsMonday, November 05, 2012

Lecture 19 Page 1

Recall: Linear Programming is a method used to compute the optimal value (minimum or maximum) of an OBJECTIVE FUNCTION, subject to certain CONSTRAINTS:

Step 1: Identify your VARIABLES.Step 2: Find the OBJECTIVE function.Step 3: Find the CONSTRAINT inequalities.Step 5: Use the constraints to graph the FEASIBLE REGION. Step 5: Compute all the VERTICES (corners) of the feasible region.Step 6: Evaluate the objective function at all vertices, and identify the optimum.(The max and min of the objective function must occur at one of the vertices.)

Why does the min/max occur at vertices?

Wrapping up section 4.2

Lecture 19 Page 2

REMARKS (page 270, posted on Friday):

Lecture 19 Page 3

A harder example (unbounded region) << THIS WAS POSTED IN FRIDAY'S LECTURE NOTES>>

Lecture 19 Page 4

Lecture 19 Page 5

Section 5.1: Exponential Functions

Lecture 19 Page 6

Lecture 19 Page 7

Lecture 19 Page 8

If $3200 is invested at 5%, compounded quarterly, the balance of the account after x years is given by the function: A

1)

How much interest is earned in 5 years?

A bacteria culture quadruples its population every hour. If we start with 100 bacteria, after t hours we'll have a culture of

2)

How many bacteria do we have after 2 hours and 15 minutes? a.Sketch the graph of this function for b.

bacteria

Examples:

Lecture 19 Page 9