Math 1050 Matrix Project

Math 1050 Matrix Project
This project uses concepts learned in section 8.4 of the textbook.
As we have seen in class, matrices are often used to solve systems of equations. However, matrices can also be used to organize large amounts of information in a format which is easy to understand and manipulate. In this project, a contractor needs to give a developer a bid for a 100 house subdivision. You will organize information about the building project in matrices, and then you will use matrix algebra to find out the total cost of building the houses.
There are three styles of houses, each with two floor plans. The following table shows how many houses are needed for each style and each floor plan.
Style
Plan A
Plan B
Ranch
12
15
Tudor
8
36
Colonial
18
11
The following table shows the amounts of materials needed to build each kind of house. You will not need to incorporate the units (cubic feet, etc.) in your matrices.
Plan
Concrete (cubic yards)
Lumber (1000 board feet)
Brick (1000's)
Shingles (100 sq. ft. bundles)
A
50
4.5
24
12
B
60
6
36
16
This table shows the cost of the different materials (per unit of material).
Concrete
$135
Lumber
$2100
Brick
$650
Shingles
$82
The contractor will also need to pay workers to perform the labor associated with each kind of material. Here are the labor costs (per unit of material).
Concrete laying
$28
Framing (uses lumber)
$4500
Brick laying
$360
Roofing (uses shingles)
$450
Use the tables to construct the following matrices:
P, which tells the number of houses of each Plan required for each style
M, which tells the amount of Materials required for each plan
C, which tells the material Costs for each material
L, which tells the Labor costs for each material
P = C =
M = L =
Answer the following questions. For each question, one way to find the answer is to multiply two or three of the above matrices together.
1. What is the amount of each kind of material that must be ordered for each style of house?
Concrete Lumber Brick Shingles
Ranch:
Tudor:
Colonial:
What matrices did you multiply?
2. What are the material costs for each style of house?
Concrete Lumber Brick Shingles Total Cost
Ranch:
Tudor:
Colonial:
What matrices could you multiply to find the totals?
3. What are the labor costs for each style of house?
Concrete Lumber Brick Shingles Total Cost
Ranch:
Tudor:
Colonial:
What matrices could you multiply to find the totals?
4. What are the total costs for all 100 houses?
Total material cost:
Total labor cost:
Total overall cost:
5. If the contractor adds 18% of the total cost to cover profit and overhead, then what is the final bid for the 100 house subdivision?
6. In the real world, building a house requires much more than four different materials. Do you think it would be useful for a contractor to use matrices to store and manipulate the type of information we had in this project?