Assignment #4 - If you use desmos for any of the questions, you have to have your name on the desmos diagram along with inequalities.

1) Suppose C = x + 2y is the objective function (Cost function) in a linear programming (minimization) 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) Using the objective function line approach, find the optimal solution to the above linear programming problem. (Graph is required -feel free to use desmos - with your name on it) (6 marks)

2) a) Find the solution set for the following systems graphically and graph the objective function line on the same diagram. (8 marks)

b) Using the objective function line, determine the optimal solution to each system. (6 marks)

c) Which constraints are binding, and which ones are non-binding? (6 marks)

i) C = 2x +y

S.t. 4x + 2y 15

3x + 5y 25

x 0 y 0

ii) P = x + 3y

S.t. x + 3y 10

5x + 2y 16

2x + 3y 12

x 0 and y 0