Assume that the total revenue received from the sale of x it

Assume that the total revenue received from the sale of x items is given by, R(x) = 25 In (3x + 5), while the total cost to produce x items is C(x) = x/2. Find the number of items that should be manufactured so that profit, R(x) -C(x), is a maximum. (Hint: Set the derivative of the profit function equal to 0.) Approximately items should be manufactured to maximize the profit. (Round to the nearest integer as needed.)

Solution

R(x) - C(x)=25ln(3x+5) - x/2=F(x) F\'(x)=25*3/3x+5 -1/2 F\'(x)=0 for maximum profit 25*3/3x+5 =1/2 150=3x+5 x=48.33 ie the no of items