Set Operation : Venn Diagrams

Shade each of the following regions. a. A'UB b. (AUB)nC'

Applications of Venn Diagrams

If n(U)=75, n(A)=40, n(AnB=15 and n(B')=40 find the following. 1. n(AUB)= 2. n(B)= 3. n(A'UB)=

Probability

The sign "I LOVE MATHEMATICS" is put on the wall of the mathematics building at South Central Carolina Technical College. The letters start to fall off of the sign. Find the probability of each of the following events. 1.. The first letter that falls off is "M" . 2. The second letter that falls off is an "A" knowing tha ...continues

Linear Programming : Objective Functions and Constraints

A small manufacturing plant produces three kinds of bicycles- three speed, five speeds, and ten speeds - in two factories. Factory A produces 16 three speeds, 12 five speeds, and 30 ten speeds in one day, while factory b produces 15 three speeds, 18 five speeds, and 20 ten speeds in one day. An order is received for 30 three sp ...continues

Linear Programming And Simplex Method : Constraints

Consider the following linear programming problem: A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% Jamaican and sells for $2.00 per pound. Each pound blend B contains 35% Mocha Java and 65% Jamaican and sells for $2.25 per pound. The merchant has available 1000 pounds of M ...continues

Linear Programming

A small manufacturing plant produces three kinds of bicycles- three speed, five speeds, and ten speeds - in two factories. Factory A produces 16 three speeds, 12 five speeds, and 30 ten speeds in one day, while factory b produces 15 three speeds, 18 five speeds, and 20 ten speeds in one day. An order is received for 30 three sp ...continues

Linear Programming and the Simplex methods : Surpluses

Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is $3.00; profit on a pitcher is $4.00. Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor. Each item requires 1 unit of time in the kiln. Labor is limited to 4 hours per day a ...continues

Linear Programming and Simplex Methods : Minimization

The linear programming problem. Minimize 5x - y subject to: -2x - 2y < 12 -3x + 2y > 0 x > 0, y > 0 is equivalent to the linear programming problem: a. Maximize 5x - y subject to: -2x -2y < 12 3x - 2y < 0 x > 0, y > 0 b. Maximize 5x-y subject to: -2x -2y < 12 -3x + 2y > 0 x > ...continues

Linear Programming and Simplex Methods : Minimization based on Tableau

Consider the simplex tableau x y u v w M 1 0 3 0 0 0 10 0 0 1 0 1 0 0 0 1 -6 0 0 0 3 0 0 8 1 0 0 7 0 0 5 0 0 1 4 The tableau above is the final one in a problem to minimize -x + 2y. The minimum value of -x + 2y ...continues

Linear Programming and Simplex methods : Pivot Elements

In the following simplex tableau, the next pivot element is: x y u v M 2 1 0 5 0 20 4 0 1 8 0 32 -3 0 0 2 1 -9 a. 4 in the second row, first column b. 8 in the second row, fourth column c. 1 in the first row, second column d. -3 in the third row, first column e ...continues