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)
__________________________
