The total cost of producing w phone sets per day at Cutting Edge Electronics plant is $( ½ w2 + 70w + 50), and the price at which each set may be sold is $(100 – w). What should be the daily output of Cutting Edge Electronics so as to obtain a maximum total profit and show that the cost of producing a set is a relative minimum at that output.

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The total cost of producing w phone sets per day at Cutting Edge Electronics plant is
$( ½ w2 + 70w + 50), and the price at which each set may be sold is $(100 – w).

What should be the daily output of Cutting Edge Electronics so as to obtain a maximum total profit and show that the cost of producing a set is a relative minimum at that output. 

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