The Young Children’s Fund (YCF) is planning its annual fund-raising campaign
for its December school holiday camp for disadvantaged children. Campaign
expenditures will be incurred at a rate of Sh. 10,000 per day. From past
experience, it is known that contributions will be high during the early stages of
the campaign and will tend to fall off as the campaign continues. The function
describing the rate at which contributions are received is:
C (t) = -100t2
+ 200,000
Where t = days of the campaign
C (t) = rate at which contributions are received in shillings per day.
The fund wants to maximize the net proceeds from the campaign.
Required:
(i) The number of days the campaign should be conducted to maximize the
net proceeds. (3 marks)
(ii) The total campaign expenditure. (2 marks)
(iii) The total contributions expected to be collected. (5
marks)
(iv) Net proceeds from the campaign (1 mark)