A shop sells 500 smartphones a week for \(\$450\) each. A market survey shows that each decrease of \(\$5\) on the price will result in the sale of an additional 10 smartphones per week. What price of the smartphone would result in maximum revenue, in dollars?
Please help me. Thanks in advance!
Price of phone = 450 - 5x where x = number of $5 decreases in price
income from number of phones sold will be 500(450-5x) + 10x (450-5x)
225000 - 2500x + 4500x - 50 x^2
- 50 x^2 + 2000x + 225000 = revenue
Max occurs at - b/2a = -2000/(2*-50) = 20 reductions of $5
$350 price results in maximum revenue of $ 245000