. A bicycle manufacturer has designed a new model and has the problem of fixing

. A bicycle manufacturer has designed a new
model and has the problem of fixing the price in such a way that profits are maximised. After
an initial cost of US $50000 to set up the production line it will cost US $85 in labour raw
materials and components to produce each bike. Market research suggests that the firm can hope
to sell 5000 bikes if the price is fixed at US $100 but they
can only expect to sell 1000 if the price is US $200 per bike. They assume the
relationship between price and demand is linear
between these two extremes. How many bikes would you advise the
company to manufacture and at what price should they be sold?