Problem 2 Optimization (50 points) The Computer Company Product (hours/unit) Labor-Hours The Management of the Computer Company Department Laptop 1 Laptop 2 Available is trying to determine the optimal weekly production amount Hardware Assembly 10 3.5 120 amount of the two laptops over the coming planning Software Instalation 3 2 56 period. The information concerning labor Testing 2 5 50 availability, labor utilization, and product Profit contribution/unit $305 $155 profitability is given in the table on the right. Neither laptop should account for more than 60% of the entire production. a) Determine the optimal production quantities. b) If overtime can be scheduled, which department would you recommend for scheduling overtime? How much would you be willing to pay per hour of overtime in each department? c) Do you need to revise your production plan if profit per unit of Laptop 1 goes down from $305 to $295. What happens with the profit? d) An engineer is willing to work two extra hours in testing for a pay $50 per hour. Is it profitable to higher an engineer?