1. 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.

1. 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)

2. Will the optimal solution you found in part a remain optimal if coefficient of x changes to 1 in the objective function (yes or no)? How do you know? explain in words not in equations or graphs. (3 marks)

3. Will the solution remain optimal is amount of Resource 2 changes to 20(yes or no)? How do you know? explain in words not in equations or graphs. (2 marks)