# For problems below, consider t

For problems below, consider the linear program below:

Maximize z = 7x + 4y

Such that And

x + 2y <= 6

3x + y <= 8
x >= 0, y >= 0

• There is an extreme point in the feasible region such that x + 2y < 6 and 3x + y < 8. What is it?

• There is an extreme point in the feasible region such that x + 2y < 6 and 3x + y = 8. What is it?

• There is an extreme point in the feasible region such that x + 2y = 6 and 3x + y < 8. What is it?

• There is an extreme point in the feasible region such that x + 2y = 6 and 3x + y = 8. What is it?

• What is the value of z, the objective function, at the optimum of the linear program?

• Using the constraints above, suppose we want to maximize w = 6x + by. There are two values of b such that the optimal set is a line segment instead of a single point. What are those two values?

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