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 111E

(a)

To determine

The formula for the number of seats sold in the flights.

Expert Solution

Answer to Problem 111E

The formula for number of seat is 13P+5603_.

Explanation of Solution

Given:

The number of seats sold at ticket price of $200 is 120. When the price of seat is increased by $3 , the number of seats sold decrease by one.

Calculation:

In the linear model f(P)=aP+b, let f(P) denote number of seats sold for price P dollars.

Since the number of seats sold at ticket price of $200 is 120, the linear model will be of with f(P)=120 and P=200. That is, 120=200a+b.

When the price of seat is increased by $3, the number of seats sold decrease by one. That is, when price is P=200+(1×3) the number of seats becomes 119. That is, 119=203a+b

Equating 120=200a+b and 119=203a+b as follows:

120=200a+b119=203a+b_1=3aa=13

Substitute a=13 in 120=200a+b and obtain b as follows:

120=200(13)+b360+2003=bb=5603

Substitute a=13 and b=5603 in f(P)=aP+b to obtain the formula for the number of seats:

f(P)=13P+5603

So, the formula for the number of seats is 13P+5603_.

(b)

To determine

The range of ticket prices for the given number of seats.

Expert Solution

Answer to Problem 111E

The range for the ticket prices is from $215_ to $290_.

Explanation of Solution

Given:

The number of seat sold for this flight range is 90 to 115.

Calculation:

From part (a), The formula for ticket price is f(P)=13P+5603.

Substitute the value 90 for f(P) in the f(P)=13P+5603.

90=13P+5603270=P+560P=560270P=$290

Substitute the value 115 for f(P) in the f(P)=13P+5603.

115=13P+5603345=P+560P=560345P=$215

Therefore, the range for the ticket prices is from $215_ to $290_.

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