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tamu Math 140 final | Questions and answers | Latest 2024/25 $10.49   Add to cart

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tamu Math 140 final | Questions and answers | Latest 2024/25

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tamu Math 140 final | Questions and answers | Latest 2024/25

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  • May 27, 2024
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  • Tamu Math 140
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tamu Math 140 final | Questions and answers | Latest 2024/25 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 whe re 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 f orm 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 ca n 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 - represe nted 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) A^-1(A)=In objective function subject to - the function we are maximizing or minimizing subject to constraints in the form of inequalities Steps to graphing an inequality. - 1. Replac e (temporarily) the inequality sign by an equal sign and graph the line. If the inequality is < or >, use a dashed line. If the inequality is ≤ or ≥, use a solid line. 2. Shade the side of the line that satisfies the inequality, i.e. that makes the inequal ity true. Label the solution set/feasible region S. corner points - -the points where the boundary line of the region changes -easiest way to find points is to set the two lines equal to one another to solve where they intersect Method of Corners - 1. Graph the feasible region. Label it S. 2. Find the coordinates of all corner points. 3. Evaluate the objective function at each corner point. 4. Find the corner point(s) that gives the maximum or minimum value (if one exists). (a) If there is only one ve rtex where the max/min is attained, this is the unique solution. (b) If the objective function is optimized at two adjacent vertices of S, then it is optimized at EVERY point along the line segment connecting these two vertices. In this case, there are infinitely many solutions. basic variable - column is one that co nsists of ones and zeroes only

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