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Dell manufactures many types of personal computers, including high-end gaming systems. Given the intense computing power necessary to render graphics in games, these systems can generate extreme amounts of thermal energy and therefore, require reliable and efficient cooling. Currently, there are three cooling systems available for these high-end systems the model G300, G550, and G700. The following table provides information for the number of components and manufacturing time per model. Model Number of Fans Number of Cooling Manufacturing Time Coils (hours) G300 1 1 8 G550 1 2 12 G700 2 4 16 Component costs for each fan is $7, while every cooling coil costs $4. The hourly rate for manufacturing is $12. Units of the G300 cooling systems retail for $170, units of G550 cooling systems retail for $254, and units of G700 retail for $357. The company has 200 fans, 320 cooling coils, and 2400 hours of manufacturing time available. How many G300, G550, and G700 cooling systems should Dell produce to maximize profits? 1. Develop an algebraic model, including objective function and all constraints, for the above problem. 2. Create an Excel model and find the optimal solution using Excel's Solver. 3. Which constraints are binding? Which constraints have slack? 4. For the optimal solution, what are the total costs to manufacture each product? 5. If the constraint on fans could be increased by 10, what would be the effect on overall profit? 6. Provide an analysis of the sensitivity report discussing the effects of reduced cost, shadow price, and the allowable increase/decrease of constraints on the optimal solution