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Linear Programming - Simplex Methods (Finite Mathematics)

1. The feasible set of a certain linear programming problem is given by the following system of linear inequalities.

x + 3y (less than or equal to symbol) 6
x - y (less than or equal to symbol) 2
- 5x + y (less than or equal to symbol) 2

Without graphing this set, determine which of the following points is not in the feasible set:

a. (3,1)
b. (1,1)
c. (-1,2)
d. (0,0)
e. all of the above

2. A certain linear programming problem has the feasible set:

x + 2y (less than or equal to symbol) 6
x - y (greater than or equal to symbol) 5
x (less than or equal to symbol) 3

Which of the following is not the feasible set?

a. ((2, -3)
b. (-1, -8)
c. (3, -4)
d. (0, 1)
e. e. none of the above

3. Consider the following linear programming problem: A coffee merchant sells two blends of coffee. Each blend of pound A contains 80% Mocha Java and 20 % Jamacian and sells for $2 a pound. Each pound blend B contains 35% Mocha Java and 65% Jamacian and sells for $2.25 a pound. The merchant has available 1000 pounds of Mocha Java and 600 pounds of Jamacian. The merchant will try to sell the amount of each blend that maximizes her income. Let X be the number of pounds of blend A and Y be the number of pounds of blend B. The objective function is:

a. .35x + 2y
b. .80x + .20y
c. 2.25x + .2y
d. 1000x + 600y
e. none of the above

4. Consider the following linear programming problem: New cars transported from docks in Baltimore and New York to dealerships in Pittsburgh and Phili. The dealership in Pittsburgh needs 20 cars and the dealership in Phili needs 15 cars. It costs $60 to transport a car from Baltimore to Pittsburgh, $45 to transport a car from Baltimore to Phili, $65 to transport a car from New York to Pittsburgh, $40 to transport a car from New York to Phili. There are 30 cars on the dock in Baltimore and 18 cars on the dock 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 Phili and y represents the number of cars sent from New York to Pittsburgh, then the number of cars sent from Baltimore to Pittsburgh is given by:

a. 20 - x
b. 20 -y
c. 30 -x
d. 30 - y
e. none of the above

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This solution is comprised of a detailed explanation to answer linear programming using simplex methods.

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