Linear Programming and the Simplex methods

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 and kiln time is limited to 6 units per day. Initial and final tableaux are shown in finding the production plan which will maximize profits: (x = number of vases and y = number of pitchers made per day). X y u v M x y u v M ½ 1 1 0 0 4 0 1 2 -1 0 2 1 1... click for more

Linear Programming and Simplex Methods

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 > 0, y > 0 c. Maximize 5x -y subject to : ] -2x -2y < 12 -3x + 2y < 0 x > 0, y > 0 d. Maximize 5x-y subject to: -2x -2y < 12 3x + 2y > 0 x > 0, y > 0 e. None of the above

Linear Programming and simplex methods

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 occurs when: a. x = 10, y =3 b. x = -10, y= -3 c. x = 10, y =0 d. x = -20, y= 6. e. None of the above

Linear Programming and Simplex methods

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. None of the above

Linear Programming and Simplex Methods

Problem: New cars are transported from docks in Baltimore and New York to dealerships in Pittsburgh and Philadelphia. The dealership in Pittsburgh needs 20 cars and the delaership in Philadelphia needs 15 cars. It costs $60 to transport a car from Baltimore to Pittsburgh, $45 to transport a car from Baltimore to Philadelphia, $65 to transport a car from New York to Philadelphia. There are 30 cars on the docks in Baltimore and there are 18 cars on the docks in New York. The number of cars sent from each dock to each dealership is chosen to minimize total transportation costs. If x represents the number of cars sent from Baltimore to Philadelphia and y represents the number of cars sent... click for more