Question

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.

Answer 1

The function that represents this company’s profit f(x) depends on the number of items sold is$\rm f(x)=-2(x-105)^2+18050$  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,

$\rm f(x)=profit\\\\f(10)=1$

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,

$\rm f(105)=18050$

Differentiate the function

$\rm f'(105)=0\\\\And \ f''(105)=0$

The function which satisfies all the conditions is,

$\rm f(x)=-2(x-105)^2+18050$

Hence, The function that represents this company’s profit f(x) depends on the number of items sold is $\rm f(x)=-2(x-105)^2+18050$.

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Answer 2

Answer:

The answer is B. f(x)=−2(x−105)2+18,050

Step-by-step explanation: