Answer: 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.