Question $2$: $25$ Marks

A farmer has $20$ hectares for growing barley and swedes. The farmer has to decide how much of each to grow. The cost per hectare for barley is $$30$ and for swedes is $$20.$ The farmer has budgeted $$480.$ Barley requires $1$ man$-$day per hectare and swedes require $2$ man$-$days per hectare. There are $36$ man$-$days available. The profit on barley is $$100$ per hectare and on swedes is $$120$ per hectare. Determine the number of hectares of each crop the farmer should sow to maximize the profits. Use GNU Octave to determine the maximization value as well as the point at which the maximum occurs.