1. Describe the region of feasible solutions for the following system of inequalities:

For this system of inequalities in Task 1, suppose the objective function is defined as P = 6x + 8y. Find the maximum value for P, and the minimum value for P, subject to the constraints of the region of feasibility.

2. Choose a linear programming problem from your textbook, and solve it. Describe this problem, and its solution.

a) Using this problem as your example, describe what the different parameters in the objective function represent?

b) Choose three points within the region of feasible solutions. What is different in the objective function for each of those three points? Why does this change for different points?

3. In trying to maximize or minimize the objective function P, why do you slide the line? When you move the line to maximize or minimize the function, why must you move the line so that it always remains parallel to itself?

4. Why can P not be maximized if the objective function goes through the middle of the region of feasible solutions? Conversely, why is the maximum or minimum of an objective function represented by a line that intersects a vertex of the region of feasible solutions? Could the maximum occur along one of the edges of the region? Explain why or why not.