Each Alpha sold yields a net profit of $385, each Beta sold yields a net profit of $545, and each Gamma sold yields a net profit of $635. In addition, the manager of the test facilities has improved A-line testing procedures so that each Alpha requires 0.85 hour, whereas each Beta requires 0.65 hour. Testing a Gamma laptop still requires one hour. Finally, the production manager has hired additional personnel and there are now 2250 hours available each week for assembly of the three computers. 120 hours and 48 hours are respectively available on the A-line and the C-line for testing purposes each week.(1) Write an optimization model(2) Which capacities would you consider expanding to generate further profits? Which would not change your optimal solution even if they were expanded?(3) Management would like to make sure that at least 20 Gammas are produced because of some ongoing contract. Revise your model. What is a new optimal solution with this additional requirement?