1. A vitamin manufacturer wants to produce a vitamin A elixir. There are two sources of vitamin A, xylocol and yellow gel. The manufacturer wants to produce 10 ml. bottles of the elixir and wants each bottle to cost less than $12. Xylocol costs $2 per ml. and yellow gel costs $1 per ml. The process used requires more yellow gel than xylocol. If xylocol produces 3 mg. of vitamin A per ml. and yellow gel produces 1 mg. of vitamin A per ml., how many ml. of each should be used to maximize the output of vitamin A?
2. A manufacturer produces two items, bookcases and library tables. Each item requires processing in each of two departments. Department 1 has 40 hours available and department 2 has 36 hours available each week for production. To manufacture a bookcase requires 2 hours in department 1 and 4 hours in department 2 while a library table requires 3 hours in department 1 and 2 hours in department 2. Profits on the items are $6 and $7 respectively. If all the units can be sold, how many of each should be made to maximize profits?