Olympic Bike company is introducing two new lightweight bicycle frames, the Deluxe and the Professional, to be made from special aluminium and steel alloys. The anticipated unit profits are $10 for the Deluxe and $15 for the Professional. The number of pounds of each alloy needed per frame is summarized in the table below. A supplier delivers 100 pounds of the aluminium alloy and 80 pounds of the steel alloy weekly.

	Aluminium Alloy	Steel Alloy
Deluxe	2	3
Professional	4	2

• Task 1

1. Model the above problem as an optimization problem maximizing the weekly profit contribution:
   1. define the decision variables
   2. define the objective function
   3. state the constraints

2. Solve the problem using Excel Solver

• Task 2
  1. Suppose the profit on deluxe frames is increased to $20. Update the model you created for Task-1 with the new value.

Is the above solution in task 1 still optimal (the value of the decision variables still the same)? What is the value of the objective function when this unit profit is increased to $20?

2. Based on the value of the objective function after the change, what is your suggestion for the company? Justify your answer.