INSTRUCTIONS:

1. The
paper has two
2. sections. Section Ais
Attempt any other twO
3. compulsory.
Show all your workingsquestions in Section B.
clearly.
SECTION A
QUESTION ONE (25 MARKS)
a. A former BCom student
launcheda nrivatelv ownedcompany specializing n the
Of steel. bars. The company sets
prouction schedules on yearly basis broken down produvuo
quarterly calendar. The demand for the bars is quite variable, by a
and third quarters. Production costs vary from being at a peak in the second
quarter
Ihe company is planning for only one vear and the
to quarter due to a variety of reasons.
relevant details of the company's situation. Further,information
the
table below sets forth all the
bar from one season to the company incurs Kshs 30 to store a
next.

Quarter 1 2 3
Demand (000 bars) 30 90 70 10
Cost/bar (Kshs) 1,000 1,200 1,500
Plant capacity ("000'bars) 1,000
60 60 60 60

Set up a linear programming model which will

satisfying demand. (DO NOT SOLVE THE MODEL). minimize total production costs while
(12 Marks)
b. A manufacturing frm produces two products X and Y.
To determine the units to be produced
in order to minimize production cost, a
linear programming model was formulated.
 However, the
method. Below Production
is an Manager did not have adequate time to compBete the simplex
intermediate tableau nroduced by the Manager.

C 3
C Basic 0 M
X X
Variable S S, A B
Si
(0 1 1
S. 20
M 1 1
A 12
4 0 -1 8
Z 4M M -M M 8M
C-Z 3-4M 5-M M

Required:
i. Complete the simplex
ii. How many units of X
method for the Production Manager (6 Marks)
ii. How many units of Y
should the company produce? (2Marks)
iv. What is the minimum
should the company produce? (2 Marks)
production cost? (3 Marks)

QUESTION TWO(25 MARKS)

a. EOQ models, however complex, are restricted by so many assumptions that they
limited practical value." Do you agree with this have very
statement? Illustrate your answer.
b. The office manager of the Metro Life (8 Marks)
lnsurance company orders letterhead stationery from
an office products firm in boxes of 500 sheets.
The company uses 6500 boxes per year.
Annual carrying costs are Ksh. 30 per box and ordering cost are Ksh. 280.
The discount price
schedule is provided by the office supply in the table below.
Order Quantity (boxes) Price per box (Kshs)
200-999 160
1000-2999 140
3000-5999 130
6000-Above 120

Required:
Determine the optimal order quantity and the total annual inventory costs. (17 Marks)
SECTION B(ANSWER ANY TWO QUESTIONS)
QUESTION THREE (25 MARKS)
An enginecring firm intends to launch a new
product in the market. The activities required in the
design and manufacture of the product are listed below together with their
associated costs. In addition, for each day the project is ongoing, there is adurations in days and
daily charge of Ksh
2,000.
Activity Preceded Most
By likel Norma Cras Crash
Optimisti Pessimisti ICost Cost
c time time c Time (Kshs) time (Kshs)
A 6 6 6 1400
<aA B A, J, M, L 6 6 1800
1600
2300
6 18 24 1800 12 3000
6 12 12 2200
-- 12 12 24 3000
9 2500
3000
12 18 30 3000 18 3900
K C 6 12 12 4000 10 4500
G 6 12 18 1900 10 2300
H B, E 6 12 18 2500 10 3200
G 12 18 18 180 16 280
J C, D 6 12 18 1800 2100
L 6 12 18 1900 10 2300
M K 6 18 24 1800 12 3000

Required:
a. Draw anetwork diagram and determine the normal project completion time and the
associated cost. (12 Marks)
b. Determine the probability that the project will be completed in 75 days. (5 Marks)
c. Using crash time and cost determine the minimum costs of completing the project in 78 days.
(8 Marks)

QUESTION FOUR (25 MARKS)

EAN has three manufacturing plants in Nairobi, Kisumu and Mombasa with production capacity
of 200, 300 and 500 respectively. The firm also has three warehouses in location 1, 2 and 3. The
demand for each of the warehouses is 500, 150 and 200 respectively. The cost of transporting
one unit from Nairobi to warehouses 1,2, and 3 is Ksh 6, 8 and 15 respectively. Cost of
transporting one unit from Kisumu to warehouses 1, 2, and 3 is Ksh 3,4 and 12 respectively.
Further, the cost of transporting one unit from Mombasa to warehouses 1, 2, and 3 is Ksh 5, 3
and 18 respectively. Using the North west method as the starting point, advice the management
on how they should transport the goods from the plants to the warehouses.
QUESTION FIVE (25 MARKS)
a. Discuss the advantages and limitations of
simulations (8 Marks)
b. Mavuno Farmers Society is considering the
planting of wheat on a piece of land it
acquired. The data below relates to the estimated selling prices, yield and cost of recently
wheat, which is done oncea year.
planting the
Selling Price Yield Per Cost Per
Per Tonnes Acre Acre (Sh.
(Sh. 000) Probability (Tonnes) Probability "000) Probability
240 0.18 70 0.09 12,000 0.14
250 0.29 75 0.16 14,000 0.22
260 0.31 80 0.24 16,000 0.36
270 0.14 85 0.38 18,000 0.26
280 0.08 90 0.13 20,000 0.02

Required:
i. Simulate the profits of the society for 8years, showing the profit for each year.
(14 MarkS)
i. Determine the average annual profit. (3Marks)
Assign the RNs beginning with 00
Random Numbers;
Selling Price; 03,91, 38, 55, 17,46, 32, 43
Yield; 69, 72, 24, 22, 61, 96, 30,32
Cost; 02, 88, 25,39, 63, 37, 53, 15
[Total-25 Marks)
 Table of the standard normal distribution values (z0)
0.09
0.04 0.05 0.06 0.07 0.08
0.00 0.01 0.02 0.03
.51994 0.52392 0.52790 0.53188 0.53586
0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.56749 0.57142 0.57535
0.55962 0.56356
0.1 0.53983 0.54380 0.54776 0.55172 0.55567 0.60642 0.61026 0.61409
0.59871 0.60257
0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.64058 0.64431 0.64803 0.65173
0.63307 0.63683
0.3 0.61791 0.62172 0.62552 0.62930 0.68439 0.68793
0.67364 0.67724 0.68082
0.65542 0.65910 0.66276 0.66640 0.67003 0.71904 0.72240
0.4 0.70540 0.70884 0.71226 0.71566
0.5 0.69146 0.69497 0.69847 0.70194 0.74537 0.74857 0.7$175 0.75490
0.73237 0.73565 0.73891 0.74215
0.6 0.72575 0.72907 0.77337 0.77637 0.77935 0.78230 0.78524
0.77035
0.7 0.75804 0.76115 0.76424 0.76730 0.80511 0.80785 0.81057 0.81327
0.79673 0.79955 0.80234
0.8 0.78814 0.79103 0.79389 0.82894 0.83147 0.83398 0.83646 0.83891
0.82121 0.82381 0.82639
0.9 0.81594 0.81859 0.85314 0.85543 0.85769 0.85993 0.86214
0.84614 0.84849 0.85083
1.0 0.84134 0.84375 0.87493 0.87698 0.87900 0.88100 0.88298
0.86864 0.87076 0.87286
1,1 0.86433 0.86650 0.89435 0.89617 0.89796 0.89973
0.90147
0.88877 0.89065 0.89251
1.2 0.88493 0.88686 0.91149 0.91308 0.91466 0.91621
0.91774
0.90658 0.90824 0.90988
1.3 0.90320 0.90490 0.92647 0.92785 0.92922 0.93056
0.93189
0.92220 0.92364 0.92507
0.91924 0.92073 0.94179 0.94295 0.94408
1.4
0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.95254 0.95352 0.95449
1.5 0.94845 o.94950 0.95053 0.95154
0.94520 0.94630 0.94738 0.96164 0.96246 0.96327
1.6
0.95637 0.95728 0.95818 0.95907 0.95994 0.96080
1.7 0.95543 0.96856 0.96926 0.96995 0.97062
0.96485 0.96562 0.96638 0.96712 0.96784
1.8 0.96407
0.97381 0.97441 0.97500 0.97558 0.97615 0.97670
0.97193 0.97257 0.97320
1.9 0.97128 0.98030 0.98077 0.98124 0.98169
0.97831 0.97882 0.97932 0.97982
0.97725 0.97778 0.98500 0.98537 0.98574
2,0
0.98257 0.98300 0.98341 0.98382 0.98422 0.98461
2.1 0.98214 0.98778 0.98809 0.98840 0.98870 0.98899
0.98679 0.98713 0.98745
2.2 0.98610 0.98645 0.99086 0.99111 0.99134 0.99158
0.98956 0.98983 0.99010 0.99036 0.99061 0.99343 0.99361
0.98928
2.3
0.99224 0.99266 0.99286 0.99305 0.99324
0.99245
0.99180 0.99202 0.99492 0.99506 0.99520
2,4
0.99413 0.99446 0.99461 0.99477
0.99430
2.5 0.99379 0.99396
0.99598 0.99609 0.99621 0.99632 0.99643
0.99560 0.99585
0.99573
0.99534 0.99547 0.99711 0.99720 0.99728 0.99736
2.6
0.99664 0.99674 0.99693 0.99702
0.99683 0.99807
2.7 0.99653 0.99781 0.99788 0.99795 0.99801
'o.99744 0.99752 0.99760 0.99767 0.99774 0.99851 0.99856 0.99861
2.8 0.99841 0.99846
0.99813 0.99819 0.99825 0.99831 0.99836 0.99896 0.99900
2.9 0.99886 0.99889 0.99893
0.99865 0.99869 0.99874 0.99878 0.99882 0.99924 0.99926 0.99929
3.0 0.99918 0.99921
0.99903 0.99906 0.99910 0.99913 0.99916 0.99944 0.99946 0.99948 0.99950
3.1 0.99942
0.99931 0.99934 0.99936 0.99938 0.99940 0.99960 0.99961 0,99962 0.99964 0.9996s
3.2
0.99952 0.99953 0.99955 0.99957 0.99958 0.99974 0.99975 0.99976
3.3
0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99983 0.99983
34 0.99980 0.99981 0.99981 0.99982
3.5 0.99977 0.99978 0.99978 0.99979