The national office of a car rental company is planning its maintenance for the
next year. The company’s management are interested in determining the
company’s needs for certain repair parts. The company rents saloon cars,
station wagons and double cab pick-ups. The matrix N shown below indicates
the number of each type of vehicle available for renting in the four regions of
the country.
Saloons Station Double
Wagons cabs
160 400 500 Coast
N = 150 300 200 Central
100 100 150 Western
120 400 300 Highlands

Four repair parts of particular interest, because of their cost and frequency of
replacement, are fan belts, spark plugs, batteries and tyres. On the basis of
studies of maintenance records in different parts of the country, the
management have determined the average number of repair parts needed per
car during a year.
These are summarized in matrix R below:
Saloons Station Double
Wagons cabs
17 16 15 Fan belts
R = 12 8 5 Plugs
9 7 5 Batteries
4 7 6 Tyres
Required:
(i) The total demand for each type of car. (3 marks)
(ii) The total number of each repair part required for the fleet. (3
marks)
(iii) If matrix C below contains the cost per unit in shillings for fan belts,
spark plugs, batteries and tyres, calculate the total costs for all repair
parts.
C = (1250, 800, 6500, 8000) (3 marks)