The manager of a company uses the function shown to model the company’s daily profit based on the price of a product in dollars, x. f(x)=(x-22)(53-x) what is the minimum price, in dollars, to avoid a loss? what is the maximum price, in dollars, to avoid a loss? what is the price, in dollars, that results in the greatest profit?

1) The minimum price, in dollars, to avoid a loss = 22,

2) the maximum price in dollars , to avoid a loss = 53,

3) The price that results the maximum profit = 37.5 dollars

Step-by-step explanation:

Since the given function that shows the total profit,

Where x is the price of the product.

Since for avoiding the loss,

,

⇒

If

If

Thus, 53 ≥ x ≥ 22,

Therefore, the minimum price to avoid the loss = $ 22

And, the minimum price to avoid the loss = $ 53

⇒

Now, For maximum or minimum,

,

⇒

⇒

⇒

For x = 37.5, f''(x) is negative,

Thus, For the price of $ 37.5 dollars the company has the greatest profit.