The book manufacturer can sell 30 books at a price of $5 per unit. When the price increases to $10, there are 20 books sold. The cost of the book manufacturer includes $100 and $2 variable cost per unit.

a. Express the profit function with respect to the quantity

b. Find the gradient of the total revenue and how much increase (decrease) in total revenue when there is 2 units increase at the current units of 25 units.

c. Find the gradient of the profit function at the current quantity of 35 units

d. Forecast the trend of the profit of the firm at the quantity of 50 units. Give the comment on whether the firm should sell one more book to increase the profit