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.