A small shop located in Utica sells a variety of dried fruits and nuts. The shop caters to travelers of all types; it sells one-pound boxes of individual items, such as dried bananas, as well as two kinds of one-pound boxes of mixed fruits and nuts, called "Trail Mix" and "Subway Mix".

Because of the health inspection issues, individual items and mixed items can only be sold as packaged one-pound boxes. Here are the amounts of current supplies:

Item

Dried Bananas 800 pounds

Dried Apricots 600 pounds

Coconut Pieces 500 pounds

Raisins 700 pounds

Walnuts 1200 pounds

The selling prices of the various types of boxes offered are:

Trail Mix $9 per box

Subway Mix $12 per box

Dried Bananas $5 per box

Dried Apricots $8 per box

Coconut Pieces $10 per box

Raisins $6 per box

Walnuts $15 per box

The manager would like to obtain as much revenue as possible from selling these boxed products. The management also decided that no more than 70% but at least 30% of these boxed products should be allocated to the Mixes. The Trail Mix consists of equal parts of all individual items, whereas the Subway Mix consist of 2 parts of walnuts and one part each of dried bananas, raisins, and coconut pieces. There are no dried apricots in the Subway Mix.

1.) Formulate and list the linear program for this problem. Report your production decision and its dereived revenue.