This problem was contributed by Dr. Rick Wilson of Oklahoma State University.

The recent drought has hit farmers hard. Cows are eating candy corn!

You are interested in creating a feed plan for the next week for your cattle using the following seven nontraditional feeding products: Chocolate Lucky Charms cereal, Butterfinger bars, Milk Duds, vanilla ice cream, Cap’n Crunch cereal, candy corn (because the real corn is all dead), and Chips Ahoy cookies.

Their per pound cost is shown, as is the protein units per pound they contribute, their total digestible nutrients (TDN) they contribute per pound, and the calcium units per pound.
You estimate that the total amount of nontraditional feeding products contribute the following amount of nutrients:
at least 20,000 units of protein, at least 4,025 units of TDN, at least 1,000 but no more than 1,200 units of calcium.
There are some other miscellaneous requirements as well.
• The chocolate in your overall feed plan (in pounds)
cannot exceed the amount of nonchocolate poundage.
Whether a product is considered chocolate or not is shown in the table (YES = chocolate, NO = not chocolate).
• No one feeding product can make up more than 25%
of the total pounds needed to create an acceptable feed mix.
• There are two cereals (Chocolate Lucky Charms and Cap’n Crunch). Combined, they can be no more than 40% (in pounds) of the total mix required to meet the mix requirements.
Determine the optimal levels of the seven products to create your weekly feed plan that minimizes cost.
Note that all amounts of products must not have

Choc Lucky Vanilla Ice Charms Butterfinger Milk Duds Cream Cap'n Crunch Candy Corn Chips Ahoy $$/lb 2.15 7 4.25 6.35 5.25 4 6.75 Choc YES YES YES NO NO NO YES Protein 75 TDN 12 20 Calcium 3 824 80 45 65 72 26 62 18 6 || 8 4.5 12 2 255 12