Chapter 3 practice test Optimization

Thinking:

1. The radius and height of a tank cannot exceed 5 m and 12 m respectively. Is it possible to construct a tank with a volume of 900 m3? If it is possible, what are the restrictions on its radius? (6 marks)

Communication:

1. A landlord manages 100 apartments in a complex downtown and charges his tenants monthly. When the rent is $800 a month, all of the apartments are rented. For every $15 increase in rent, one apartment becomes empty. On average, each apartment needs $60 invested in maintenance and repairs each month. The landlord wants to know how much he should charge per month in order to have the greatest profit. Could he make a greater profit without all of the apartments rented? Explain. (6 marks)