This investigation concerns the production of cycles.
a CNY Works, an experienced cycle manufacturing company has designed a revolutionary bicycle which is about to be put into production. The Board has met to discuss the selling price of the CNY bike as the marketing division believes that this will strongly influence the number sold and hence the production ordered.
The Marketing Director estimates that if the selling price is fixed at $300, then 5500 bicycles will be sold in the first month whereas if the price is $600, only 1000 will be sold. What should the selling price be in order to maximise sales revenue. For example, if the selling price is $300 then the sales revenue is 5500 × $300 = $1,650,000.
How many cycles should be produced to acheive this?
b The firm introduces a second bicycle, more expensive than the first but also more attractive. As a result of market research, the Managing Director believes that the relationship between the selling price (t) and the number sold (m) per month will be:
Investigate what the joint production per month for the two bicycles should be to maximise the sales revenue.
c If there is an upper limit (e.g. 10 000) on the size of the joint monthly production, investigate what difference this will make.
Reproduced from the Scottish Certificate of Education (permission pending)