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 7 nontraditional feeding products: Chocolate Lucky Charms cereal, Butterfinger bars, Milk Duds, Vanilla Ice Cream, Cap’n Crunch cereal, Candy Corn (since 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 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 non-chocolate 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 percent of the total pounds needed to create an acceptable feed mix.
• There are two cereals (Choco Lucky Charms and Cap’n Crunch). Combined, they can be no more than 40 percent (in pounds) of the total mix required to meet the mix requirements. Determine the optimal levels of the 7 products to create your weekly feed plan that minimizes cost. Note that all amounts of products must NOT have fractional values (whole numbered pounds only).

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$$/lb choc Protein TDN Calcium Choc Lucky Charms 2.15 05 75 12 3 YES Butterfinger 7 YES 80 20 4 Milk Duds 4.25 YES 45 18 4.5 Vanilla Ice Cream 6.35 NO 65 6 12 Cap'n Crunch 5.25 NO 72 11 2 Candy Corn 4 NO 26 8 1 Chips Ahoy 6.75 YES 62 12 5