## Fall 2001

## Project 1

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?