Q:

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x? f(x)=−2(x+105)2+18,050 f(x)=−2(x−105)2+18,050 f(x)=−10(x+105)2+18,050 f(x)=−10(x−105)2+18,050 HEELLPP IM BEING TIMED 79 POINTS

Accepted Solution

A:
The function that represents this company’s profit f(x) depends on the number of items sold is[tex]\rm f(x)=-2(x-105)^2+18050[/tex]  and it can be determined by using the properties of the function.Given that,According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold.What is the function?Let, x be the amount sold,According to one company’s profit model, the company has a profit of 0 when 10 units are sold.Then,The function represents the company has a profit of 0 when 10 units are sold is,[tex]\rm f(x)=profit\\\\f(10)=1[/tex]The maximum profit of $18,050 when 105 units are sold.Therefore,The function represents the maximum profit of $18,050 when 105 units are sold is,[tex]\rm f(105)=18050[/tex]Differentiate the function[tex]\rm f'(105)=0\\\\And \ f''(105)=0[/tex]The function which satisfies all the conditions is,[tex]\rm f(x)=-2(x-105)^2+18050[/tex]Hence, The function that represents this company’s profit f(x) depends on the number of items sold is [tex]\rm f(x)=-2(x-105)^2+18050[/tex].To know more about Equation click the link given below.brainly.com/question/1995928