Problem Statement A:

A small shop located in Boston 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 one-pound box 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 quantities of current supplies:

Item

Dried Bananas800 pounds

Dried Apricots600 pounds

Coconut Pieces500 pounds

Raisins700 pounds

Walnuts1200 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 make as much revenue as possible from selling these boxed products.

The manager decided that no more than 70% but at least 35% of these boxed products should be allocated to the mixes (Trail Mix and Subway Mix).

The Trail Mix consists of equal parts of all five individual items, whereas the Subway Mix consist of 2 parts of walnuts and one part each of dried bananas, raisins, and coconut pieces.There is no driedapricots in the Subway Mix.

Required Answers:

- Formulate the linear program for this problem. Clearly define your decision variables and list the objective function with its associated constraints.