A company plans to produce a new gadget. The cost to produce one unit is $50, and the company sells each unit for $80. The company can also choose to invest in a special manufacturing process that reduces the production cost to $40 per unit but requires an initial investment of $3000. If the company plans to produce 200 units, should they invest in the special manufacturing process? Calculate the total profit in both scenarios and determine the savings. Let's think step by step and output the final answer within \boxed{}.
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