Fill in the blank

1. A company sells its product for $44 per unit. Write an expression for the amount of

money received (revenue R) from the sale of x units of the product.

R = ________

2. Suppose a calculator manufacturer has the total cost function C(x) = 40x + 6600

and the total revenue function R(x) = 62x.

(a) What is the equation of the profit function P(x) for the calculator?

P(x) = ________

(b) What is the profit on 2400 units?

P(2400) = $ ________

3. Suppose a ceiling fan manufacturer has the total cost function C(x) = 41x + 1860

and the total revenue function R(x) = 72x.

(a) What is the equation of the profit function P(x) for this commodity?

P(x) =______

(b) What is the profit on 40 units?

P(40) = ________

(c) How many fans must be sold to avoid losing money?

______fans

4. Suppose a computer manufacturer has the total cost function C(x) = 70x + 3600 (in

dollars) and the total revenue function R(x) = 370x (in dollars).

(a) What is the equation of the profit function P(x) (in dollars) for this commodity?

P(x) =_______

(b) What is the profit (in dollars) on 338 items?

P(338) = $_______

(c) How many items must be sold to avoid losing money?

x = _______ items

5. Use the rules of exponents to simplify so that only positive exponents remain.

(Simplify your answer completely.)

a3 · a

_______________

6. Use the rules of exponents to simplify so that only positive exponents remain.

(Simplify your answer completely.)

(xy)2

___________________

7. Perform the indicated operation and simplify.

−4(4 − x2)

____________________

8. Perform the indicated operation and simplify.

(3y + 2)(2y − 3)

____________________

9. Perform the indicated operation and simplify.

(3x + 5)2

____________________________

10. Perform the indicated operation and simplify.

3(2x + 1)(2x − 1)

____________________

11. Perform the indicated operation and simplify.

(x − 9)(x2 + 9x + 81)

_____________________

12. Simplify by combining like terms.

(18pq − 9p2) + (9pq + 3p2)

__________________________