TAMU MATH 140 FINAL EXAM GUIDE 2024 WITH COMPLETE SOLUTION
cost function - C(x)=mx+b
variable cost+fixed cost
revenue function - R(x)=p*x
profit function - P(x)= R(x)-C(x)
break even quantity - R(x)=C(x) (or P(x)=0)
where revenue and cost intersect
equilibrium point - S(x)=D(x)
where supply and demand intersect
how to determine which number to pivot - 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 - when there's no more negative numbers in the bottom row
elementary operations - yield an equivalent system of equations •A matrix is in echelon form if: - 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.
Gauss elimination - procedure for a systematically using elementary
operations to reduce a system of linear equations to an equivalent system whose solution set can be immediately determined by backward substitution.
order of a matrix - m × n where m is the number of
rows and n is the number of columns.
element in the ith row and jth column of a matrix A is denoted by - A(ij)
transpose of a matrix - represented by A^T
switch the rows and the columns
row matrix - matrix with one row
column matrix - matrix with one column
square matrix - matrix with equal number of rows and columns
identity matrix - Matrix multiplication properties - A(BC) = (AB)C
A(B+C) = AB+AC
AIn= InA = A
(In is identity matrix)
cost function - C(x)=mx+b
variable cost+fixed cost
revenue function - R(x)=p*x
profit function - P(x)= R(x)-C(x)
break even quantity - R(x)=C(x) (or P(x)=0)
where revenue and cost intersect
equilibrium point - S(x)=D(x)
where supply and demand intersect
how to determine which number to pivot - 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 - when there's no more negative numbers in the bottom row
elementary operations - yield an equivalent system of equations •A matrix is in echelon form if: - 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.
Gauss elimination - procedure for a systematically using elementary
operations to reduce a system of linear equations to an equivalent system whose solution set can be immediately determined by backward substitution.
order of a matrix - m × n where m is the number of
rows and n is the number of columns.
element in the ith row and jth column of a matrix A is denoted by - A(ij)
transpose of a matrix - represented by A^T
switch the rows and the columns
row matrix - matrix with one row
column matrix - matrix with one column
square matrix - matrix with equal number of rows and columns
identity matrix - Matrix multiplication properties - A(BC) = (AB)C
A(B+C) = AB+AC
AIn= InA = A
(In is identity matrix)
