Problem 804

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72000 + 40x and p(x) = 300 – x/20 ,0≤x≤6000.

A)    Find the maximum revenue.

B)    Find the maximum profit, the production level that will realize the maximum profit, and the prices the company should charge for each television set.

C)    If the government decides to tax the company $4 for each set it produces, how many seta should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?

 

Solution:-

 

A)    The maximum revenue is $450000.

B)    The maximum profit is $266000 when 2600 sets  are manufactured and sold for $ 170 each.

C)    When each set is taxed at $4, the maximum profit is $255680 when 2560 set are manufactured and sold for $172 each.

 

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