1) Suppose P = x + 2y is the objective function (Profit function) in a linear programming (maximization) problem, where x is the number of units of product A and y is the number of units of product B. a) What does the coefficient of x represent? How about the coefficient of y? (4 marks) b) Given the linear programming problem: x + y 4 Resource 1 and 3x + y 7 Resource 2 c) What is the linear inequality that represents J unit increase in Resource 1? (2 marks) d) Using the iso-profit line approach, find the optimal solution to the above linear programming problem. (2 marks)

2) a) Find the solution set for the following systems graphically and graph the iso profit line on the same diagram. (8 marks) b) Using the iso-profit line, determine the optimal solution to each system. (2 marks) c) Which constraints are binding, and which ones are non-binding? (5 marks) i) C = x +3y ii) P = 2x + y S.t. 4x + 2y 12 S.t. x + 3y 9 3x + 5y 25 5x + 2y 15 x 0 2x + 3y 10 y 0 x 0 and y 0

3) Consider the following linear programing problem: P = 2x + 3y subject to 2x + 5y 25 Resource 1 3x + 2y 19 Resource 2 as well as x 0 and y 0. a) Use the method of corners (showing your graph and corner points) to solve this problem. (i.e. Find the number of x and y so that P is optimized) (5 marks) b) Will the optimal solution you found in part a remain optimal if coefficient of x changes to 1 in the objective function? How do you know? (3 marks) c) Will the solution remain optimal is amount of Resource 2 changes to 20? How do you know? (2 marks)