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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 14 11 8 Electricity 15 10 9 Flooring 10 7 6 (a) Find real constants Phed, 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 + €bath · Y + Co and F(x, y) = ƒbed ·x + ƒbath · y + fo describing the costs for electricity and flooring, respectively.

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 14 11 8 Electricity 15 10 9 Flooring 10 7 6 (a) Find real constants Phed, 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 + €bath · Y + Co and F(x, y) = ƒbed ·x + ƒbath · y + fo describing the costs for electricity and flooring, respectively.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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: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. =
(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.
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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