A: FUNCTION
Q1. (a) The function C (x) = 25x + 80,000 express the total cost C (x) (in K£) of
manufacturing x units of a product. If the maximum number of units which can be
produced equals 20,000, state the restricted domain and range for this function.
(b) An analysis of enrolment in MBA Parallel Programme indicates that enrolment will decline as the pool of University graduates in the country shrink. The estimates indicate that the number of applicants (y) for the coming year will behave according to the function
y = f (t) = 250 – 20t where t equals time in years measured from 1999 (t = 0)
(i) What is the expected number of applicants in 2002; 2010.
(ii) Do you think this function is accurate as a predictor indefinitely into the
future?
(c) Passengers’ volume on a small regional airline has been declining at a linear rate. In 1981 the number of passengers was 245,000; in 1986 the number was 215,000. If n equals the number of passengers using the airline per year and t equals time measured in years (t = 0 for 1981).
i) Determine the linear function n = (t).
ii) Interpret the meaning of the slope.
iii) What is the number of passengers expected to be in the year 2002?
iv) It is estimated that the airline go out of business if the volume falls below 180,000. According to your function in part (a), when will this happen.
Assume that a manufacturer can purchase a needed component from a supplier at a cost of $8 per unit, or it can invest $40,000 in equipment and produce the item at the cost of $5.50 per unit.
i) Determine the quantity for which total costs are equal for the make and buy alternatives.
ii) What is the minimum cost alternative if 15,000 units are required? What is the minimum cost?
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