Assignment #4 1) Suppose P = 3x + 4y 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 s4 Resource and 2x+y55 Resource 2 1) What is the linear inequality that represents "h" unit increase in Resource i? (2 marks) in) Write the inequality that represents "k* units of increase in Resource 2. (2 marks) 2) Find the range of values for the coefficient of "y" in the objective function of question 1, so that the optimal solution remains unchanged. (10 marks) 3) Explain the meaning of shadow pricing and binding constraints in your own words. (5 marks) 4) Consider the following linear programing problem: P=2x + 4y subject to 2x + 5y s 20 Resource 3x + 4y 17 Resource 2 as well as x 20 and 20. a) Use the method of corners (showing your graph and comer points) to solve this problem. (i.e. Find the number of x and y so that Pis optimized) Hint: If you are dealing with a bounded area, then it is a maximizing problem (11 marks) b) Will the optimal solution you found in part"a" remain optimal if coefficient of x changes to 3 in the objective function"? How do you know? (5 marks) c) What is the range of values for the coefficient of x in the objective function to keep the optimal solution unchanged? (5 marks) d) Will the solution remain optimal is amount of Resource 2 changes to 23? How do you know? (4 marks)