Univ 104 Math Exam Script Comprehensive Study Guide

UNIV 104 MATH EXAM SCRIPT
COMPREHENSIVE STUDY GUIDE

●● revenue function
Answer: R(x)=p*x


●● profit function
Answer: P(x)= R(x)-C(x)


●● break even quantity
Answer: R(x)=C(x) (or P(x)=0)
where revenue and cost intersect


●● equilibrium point
Answer: S(x)=D(x)
where supply and demand intersect


●● how to determine which number to pivot
Answer: a) Find the MOST NEGATIVE element in the last row. This
determines the pivot column. If there
are two that have the same most negative value, either one is fine.

, (b) For each POSITIVE entry above the horizontal line in the pivot
column, divide the constant on
the right side of the vertical line by the corresponding element in the
pivot column. The row
with the smallest ratio becomes the pivot row. If there is a tie between
smallest ratio, defalt goes to the one that's in the highest row.
(c) The element where the pivot column and row intersect is the pivot
element.


●● how do you know when you're done pivoting
Answer: when there's no more negative numbers in the bottom row


●● elementary operations
Answer: yield an equivalent system of equations


●● •A matrix is in echelon form if:
Answer: 1. The first nonzero element in any row is 1, called the leading
one.
2. The column containing the leading one has all elements below the
leading one equal to 0.
3. The leading one in any row is to the left of the leading one in a lower
row.
4. Any row consisting of all zeros must be below any row with at least
one nonzero element.