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(Solved): A manufacturer has been selling 1700 television sets a week at $420 each. A market survey indicates ...




A manufacturer has been selling 1700 television sets a week at \( \$ 420 \) each. A market survey indicates that for each \(
A manufacturer has been selling 1700 television sets a week at each. A market survey indicates that for each rebate offered to a buyer, the number of sets sold will increase by 190 per week. a) Find the demand function , where is the number of the television sets sold per week. b) How large rebate should the company offer to a buyer, in order to maximize its revenue? c) If the weekly cost function is , how should it set the size of the rebate to maximize its profit? Question Help: Video


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we use derivative rule to solve the problems

Solution
 A manufacturer has been selling let x= 1700 television sets a week at let P(x)= $420 each.
A market survey indicates that for each$19rebate
new price p(x)=  

offered to a buyer, the number of sets sold will increase by 190 per week.
new sale =   
therefore using these two points
  


Multiply both sides by   .
  

Simplify.
  

Move all terms not containing    to the right side of the equation.
  
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