Question 1 A building contractor has accepted orders for 5 type A houses, 7 type B houses and 12 type C houses. The contractor is familiar with the kinds of raw materials that go into each type of house. These raw materials are steel, wood, glass, paint and labour. The various quantities of steel, wood, glass, paint, and hours of labour required to build each type of house are identified in appropriate units for each type by the matrix: A B C steel wood Glass Paint 5 20 16 7 7 18 12 9 6 25 8 5 Labour 17 21 13 It is known that steel costs GHC2500 per unit, wood costs GHC1200 per unit, glass costs GHC800 per unit, paint costs GHC150 per unit, and labour costs GHC1500 per hour. a. Compute and analyze the quantity of each type of raw material that he will obtain to fulfill his contract b. Determine the total cost of raw materials for all the houses he will build. c. Determine the total cost of raw materials for all the houses he will build. d. Deduce the cost matrix. Question 2 2a) There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group? Analyze and comment on the result. 2b) A boy has to cover 4km to catch a bus. He walks part of the distance at 3km/h and runs the rest at 5km/h. If he takes 1 hour to complete the distance, how many kilometers, does he walk?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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Question 1
A building contractor has accepted orders for 5 type A houses, 7 type B houses and 12 type C
houses. The contractor is familiar with the kinds of raw materials that go into each type of house.
These raw materials are steel, wood, glass, paint and labour. The various quantities of steel,
wood, glass, paint, and hours of labour required to build each type of house are identified in
appropriate units for each type by the matrix:
Labour
17
21
13
It is known that steel costs GHC2500 per unit, wood costs GHC1200 per unit, glass costs
GHC800 per unit, paint costs GHC150 per unit, and labour costs GHC1500 per hour.
steel wood Glass Paint
5
20
16
7
7
18
12
9
6
25
8
5
A
B
C
a. Compute and analyze the quantity of each type of raw material that he will obtain to
fulfill his contract
b. Determine the total cost of raw materials for all the houses he will build.
c. Determine the total cost of raw materials for all the houses he will build.
d. Deduce the cost matrix.
Question 2
2a) There are 100 students in a hostel. Food provision for them is for 20 days. How long will
these provisions last, if 25 more students join the group? Analyze and comment on the result.
2b) A boy has to cover 4km to catch a bus. He walks part of the distance at 3km/h and runs the
rest at 5km/h. If he takes 1 hour to complete the distance, how many kilometers, does he walk?
Transcribed Image Text:Question 1 A building contractor has accepted orders for 5 type A houses, 7 type B houses and 12 type C houses. The contractor is familiar with the kinds of raw materials that go into each type of house. These raw materials are steel, wood, glass, paint and labour. The various quantities of steel, wood, glass, paint, and hours of labour required to build each type of house are identified in appropriate units for each type by the matrix: Labour 17 21 13 It is known that steel costs GHC2500 per unit, wood costs GHC1200 per unit, glass costs GHC800 per unit, paint costs GHC150 per unit, and labour costs GHC1500 per hour. steel wood Glass Paint 5 20 16 7 7 18 12 9 6 25 8 5 A B C a. Compute and analyze the quantity of each type of raw material that he will obtain to fulfill his contract b. Determine the total cost of raw materials for all the houses he will build. c. Determine the total cost of raw materials for all the houses he will build. d. Deduce the cost matrix. Question 2 2a) There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group? Analyze and comment on the result. 2b) A boy has to cover 4km to catch a bus. He walks part of the distance at 3km/h and runs the rest at 5km/h. If he takes 1 hour to complete the distance, how many kilometers, does he walk?
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