College Algebra 9th txtbk

SECTION 1–5 Quadratic Equations and Applications 93
of time is called the demand for that product. The price p of a product and the demand q
for that product are often related by a price–demand equation of the following form:
q a bp
q is the number of items that can be sold at $p per item.
The constants a and b in a price–demand equation are usually determined by using historical
data and statistical analysis.
The amount of money received from the sale of q items at $p per item is called the
revenue and is given by
R (Number of items sold) (Price per item)
qp (a bp)p
Using the price-demand
equation
EXAMPLE 9 Price and Demand
The daily price–demand equation for whole milk in a chain of supermarkets is
q 5,600 800p
where p is the price per gallon and q is the number of gallons sold per day. Find the price(s)
that will produce a revenue of $9,500. Round answer(s) to two decimal places.
SOLUTION
The revenue equation is
To get a revenue of $9,500, we substitute 9,500 for R:
5,600p 800p 2 9,500
9,500 5,600p 800p 2 0
p 2 7p 11.875 0
R qp (5,600 800p)p
5,600p 800p 2
p 7 11.5
2
2.89, 4.11
Subtract 9,500 from both sides.
Divide both sides by 800.
Use the quadratic formula with
b 7, and c 11.875.
a 1,
Selling whole milk for either $2.89 per gallon or $4.11 per gallon will produce a revenue
of $9,500.
MATCHED PROBLEM 9 If the price–demand equation for milk is q 4,800 600p,
find the price that will produce
revenues of
(A) $9,300 (B) $10,500
ANSWERS TO MATCHED PROBLEMS
1. (A) x 2, 7 (B) x 4, 5 (C) x 3 (a double root) (D) x 0, 5 3
2
4
2. (A) x 152 (B) x 2i (C) x (1 12)3
3. (A) x 2 5x 25 (B) x 2 mx (m 2 4) [x (m2)] 2
4 (x 5 2) 2
4. (A) x 4 119 (B) x (6 i13)3 or 2 (133)i
5. x (3 119)2 6. (A) No real roots (two imaginary roots) (B) Two real roots
(C) One real (double) root 7. 11 and 12 8. 15 and 20 miles per hour
9. (A) $3.29 or $4.71 (B) Not possible