BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 118E
To determine

The number of units sold by the manufacturer to earn profit of $2400.

Expert Solution

Answer to Problem 118E

The number of units sold by the manufacturer is 400x4400_.

Explanation of Solution

The formula for the Revenue is R=20x where, R is the revenue in dollars ($) and x is the number of units sold.

The formula for the Cost is C=2000+8x+0.0025x2 where, C is the cost in dollars ($) and x is the number of units sold.

Also, Profit= revenuecost and the profit to the manufacturer is $2400 or more.

Substitute R=20x and C=2000+8x+0.0025x2 in C=2000+8x+0.0025x2:

P(x)=20x(2000+8x+0.0025x2)P(x)=0.0025x2+12x2000

Since the profit to the manufacturer is $2400 or more, P(x)2400. That is,

0.0025x2+12x200024000.0025x2+12x2000+20002400+20000.00250.0025x2+120.0025x44000.0025x24800x1760000x24800x+(48002)21760000+(48002)2

Simplify further as follows:

x24800x+57600004000000(x2400)24000000       [Factor perfect square](x2400)24000000      [take sqaure roots]|x2400|20002000x24002000

Further solve the equation:

2000+2400x2000+2400400x4400

Thus, the number of units sold by the manufacturer is 400x4400_.

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