Andrea is ordering supplies for summer camp and notices the supplier has a special offer on four items on her list: caps, T-shirts, socks, and shoes. The supplier packaged these items for some special orders, and a number were returned that the supplier would like to move. There are three types of packages, I, II, III.
I contains 5 caps, 10 pairs of socks, 2 T-shirts, and 4 pairs of shoes.
II contains 5 caps, 6 pairs of socks, 3 T-shirts, and 3 pairs of shoes.
III contains 4 caps, 5 pairs of socks, 6 T-shirts, and no shoes.
Andrea estimates they will need up to 200 caps, up to 300 pairs of socks, up to 210 T-shirts, and up to 60 pairs of shoes.
Based on the special price and their published camp fees, the camp can make a profit of $6 on each package I, $5 on each package II, and $2 on each package III. How many of each type of package should Andrea order to achieve maximum profit?
A maximum profit of $ is possible if Andrea orders 15 of package I and of package III, or 20 of package II and of package III. Andrea can also achieve maximum profit from any integer coordinate on the line segment between these two solutions.