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UNIVERSITY OF NAIROBI
UNIVERSITY EXAMINATIONS 2023/2024
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF ARTS IN
PLANNING
BUR 107: QUANTITATIVE TECHNIQUES FOR PLANNERS
CONTINUOUS ASSESSMENT TEST
DATE: DECEMBER 2023 TIME: ………….
INSTRUCTIONS:
1. ANSWER ALL QUESTIONS
2. The CAT MUST BE RETURNED ON 15TH JANUARY 2023
QUESTION ONE (30MARKS)
a) Briefly, discuss the importance of quantitative techniques in Urban and Regional Planning
b) Draw a graph of the following functions
(i) Y=3x+2
(ii) Y=X2-2X-3
c) Describe various forms of functions up to third-degree polynomial
d) Solve 4x2-x-3==0 using the quadratic formula
e) Solve the following simultaneous equations using the matrix algebra
4x+3y=7
3x-2y=9
f) A planner prepares two plan alternatives, i.e., Plan A and Plan B. The cost of implementing
15% of Plan A and 10% of Plan B is Kshs. 60 million. The cost of implementing 5% of
Plan A and 8% of Plan B is Kshs. 34 million.
(iii)Express the above implementation cost of Plan A and B in the form of simultaneous
equations.
(i) What will be the cost of implementing 100% of Plan A and Plan B respectively?
(ii) Which Plan is cheaper to implement?
QUESTION TWO (20MARKS)
A Kenya chemical company is producing two products A and B. The processing times are 3 hours
and 4 hours per unit for A on operations one and two respectively and 4 hours and 5 hours per unit
for B on operations on one and two respectively. The product A can be sold at sh. 3/- profit per unit
and B at sh. 8/- per unit.
a) Formulate the objective function
b) Formulate the non-negative functions
c) Draw the linear programme graphically
d) Establish the feasible region
