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 $18 on each package I, $15 on each package II, and $6 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.