HE School of Construction and Built Environment Building Services Engineering and Civil Engineering Your Last Name 12 HE School of Construction and Built Environment Building Services Engineering and

HE School of Construction and Built Environment
Higher National Diploma in Construction and Built Environment
Building Services Engineering and Civil Engineering
Your Name
Applied Mathematics for Complex Engineering Problem
Lecturer’s Name
Date

Your Last Name 2
Task 1
Problem statement
The amount of cloth and lining used by the industrial tailor limited for a single overcoat
is 6m and 5m respectively. The amount of cloth and lining for a single jacket is 4m and 2m
respectively. We are required to determine the number of jackets and overcoats that are
manufactured in a week If the company uses 600m of cloth and 360m of lining every weak for
the manufacture of the jackets and overcoats.
Solution
Step 1
Formulate the linear equation for the cloth and lining needed for the manufacture of
cloths and overcoats in a week.
For the amount of cloth used, the linear equation is:
6 C+ 4 J =600
For the amount of lining used, the linear equation is:
5 C+2 j=360
C represents the overcoats while J represent the Jackets manufactured in a week.
Step 2
Write the linear equation in simultaneous form as below:
6 C+ 4 J =600
5C +2 J =360

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Step 3
Solve the simultaneous equation using the substitution method to obtain the number of coats and
jackets manufactured in a week.
Using the first linear equation make the number of overcoats C the subject.
6 C+ 4 J =600
C= 600−4 J
6 ... ... ... ... . equation 1
Substitute the value of C into the second linear equation and solve for the number of Jackets J:
5 C+2 J=360
5 [ 600−4 J
6 ]+2 J =360
3000−20 J
6 + 2 J =360
3000−20 J +12 J=2160
−8 J=−840
J=−840
−8 =105 Jackets
To determine the number of overcoats manufactured we substitute the value of jackets into
equation 1 above:
C= 600−4 J
6

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C= 600−4(105)
6 = 180
6 =30 overcoats
Hence, the number of Jackets manufactured in a week is 105 jackets, while the number of
overcoats manufactured in a week is 30 overcoats.
Task 2
We explain the steps needed to reduce a cubic equation to linear equation and solve two
cubic equations below to find the values of x in each case
Solution
Part A
Steps
i. Apply the rational root theorem to determine the factors of the constant term and the
leading coefficient of the cubic function.
ii. Apply the factor theorem to determine which of the factors of the constant term lead
to a solution of zero for the original cubic function.
iii. Use the factor obtained in step 2 above as the divisor for the original cubic function
(dividend) to obtain the quotient in the form of a quadratic equation.
iv. Factor the quadratic equation to obtain the remaining two linear equations.
Part B
i. f ( x )=x3−6 x2 +11 x−6
Solution