LINEAR PROGRAMMING PROBLEM $2(60$ po$$nts$).$ Show ALL work. SOLVE

There are $150$ acres of land available to raise apples and beets. It takes one day to tr$$m an acre of apples and two days to

trim an acre of beets, and there are $240$ days per year available for trimming. It takes $0\mathrm{.}3$ day to pick apples and $0\mathrm{.}1$ day to

pick beets, and there are $30$ days per year available for picking. Find the number of acres of each crop that should be

planted to maximize profit, assuming that the profit is $$90$ per acre for apples and $$75$ per acre for beets.