   Chapter 2.1, Problem 33E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Revenue Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, because of the crowding and smaller lot sizes. In fact, if it builds 40 houses in this particular development, it can sell them for $200,000 each, but if it builds 60 houses, it will be able to get only$160,000 each. Obtain a linear demand equation, and hence determine how many houses Pack-Em-In should build to get the largest revenue. What is the largest possible revenue? [HINT: See Example 3.]

To determine

To calculate: A linear demand equation for Pack-Em-In-Real-State. If it builds 40 houses in a particular development, it sells them for $2,00,000 each but if it builds 60 houses, it is able to get only$1,60,000

for each house. Also determine the no. of houses build by Pack-Em-In-Real-State to get the largest possible revenue and what will be the corresponding revenue.

Explanation

Given Information:

Pack-Em-In-Real-State builds 40 houses in a particular development, and it sells them for $2,00,000 each. if Pack-Em-In-Real-State builds 60 houses in a particular development, it is able to get only$1,60,000

for each house.

Formula Used:

The equation of a straight line is,

yy1=m(xx1)

Where m

is the slope,

The slope of straight line is given by,

m=y2y1x2x1

The relationship between Revenue and Price is,

Revenue=(Price)(Demand)R(p)=(p)(q)

Calculation:

Assume, the demand or number of houses build be given by q

and price by $p. Consider the given data, Pack-Em-In-Real-State builds 40 houses in a particular development, and it sells them for$2,00,000

each.

Represent the above word problem in terms of coordinates,

(x1,y1)(q1,p1)(q1,p1)(40,200000)

if Pack-Em-In-Real-State builds 60 houses in a particular development, it is able to get only \$1,60,000

for each house

Represent the above word problem in terms of coordinates,

(x2,y2)(q2,p2)(q2,p2)(60,160000)

The linear demand equation has the form of linear equation so evaluate it by exploiting linear equation.

The slope of straight line is given by,

m=y2y1x2x1

Or

m=p2p1q2q1

Substitute 160000

for p2

, 200000

for p1

, 40 for q1

and 60 for q2

in equation m=p2p1q2q1.

m=1600002000006040 =4000020 =2000

The linear equation is given by,

yy1=m(xx1)

Or

The linear equation is given by,

pp1=m(qq1)

Substitute 2000

for m

, 40

for q1

and 200000

for p1.

pp1=m(qq1)p200000=2000(q40)p200000=2000q+80000

Add 200000 both sides to get the equation

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