An orchadist has 10 hectares of land available for growing Fuji apples and Nashi pears. She estimates that each hectare of apples will cost $5000 to establish, and each hectare of pears will cost $20 000 to establish. She is not able to spend more than $100 000 on establishing the orchard.
It is also estimated that the profit per hectare from apples will be $4000 and the profit per hectare from pears will be $8000. What is the maximum profit the orchardist can expect? How many hectares of Fuji apples and Nashi pears should she plant to achieve this? Please show your working clearly, with an explanation for the reason behind the answer you give.
Thank you for your help.