
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:2. Home building.
When you are building a new home it is important to have an idea from the very start how
much it may cost. The price varies dramatically depending on the size and the design of the
property. Your task is to analyse the data from past construction works in order to estimate
the contribution of different components. The table below show a part of construction costs
breakdown (in thousand dollars) for three houses: the first has four bedrooms and three
bathrooms, the second has two bedrooms and two bathrooms, and the third has two bedrooms
and one bathroom.
House
4beds & 3baths
2beds & 2baths
2beds & 1baths
Plumbing Electricity
14
15
11
10
9
Flooring
10
7
6
(a) Find real constants Pbed, Pbath, Po such that P(x, y)
.
= Pbed x + Pbath y + Po equals
the plumbing costs given in the table, where x is the number of bedrooms and y is
the number of bathrooms. Similarly, find functions E(x, y) = ebed x + ebath • Y + Co
and F(x, y) fbed x + fbath · y + fo describing the costs for electricity and flooring,
respectively.
=

Transcribed Image Text:(b) In general, for a certain construction component, suppose the costs equal w₁ for the
first house, w₂ for the second house, and w3 for the third house. Find formulas for Wbed,
Whath and wo such that W(x, y) = Whed x + Wbath · y +wo gives values w₁, W2, W3 for
these three houses.
(c) Find a matrix A that W(x, y)
=
A
W1
0·0
W2
W3
where "." is the dot product of vectors.
(d) The matrix A from part (c) should be the inverse of B =
431
2 2 1 Explain why one
21 1
could expect this relation even without computing entries of A.
(e) Sketch the region of all ordered pairs of real numbers (x, y) such that 1 ≤ y ≤ x and
P(x, y) + E(x, y) + F(x, y) ≤ 30. List all points with integer coordinates lying in this
region.
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