A cereal company makes three types of grain cereal: Nutty Grains, Regular Grains, and Fruity Grains. Producing 500 boxes of Nutty Grains requires 370 pounds of whole wheat flour, 96 pounds of pecans, and 32 pounds of raisins. Producing 250 boxes of Regular Grains requires 180 pounds of whole wheat flour, 32 pounds of pecans, and 35 pounds of raisins. Producing 500 boxes of Fruity Grains requires 350 pounds of whole wheat flour, 32 pounds of pecans, and 108 pounds of raisins.

1) Set up a linear production model for this situation. Then use it for the following questions.

2) The company has available 17,020 pounds of whole wheat flour, 3,328 pounds of pecans, and 2,910 pounds for raisins. How many boxes of each type might the company need to produce in order to use all of these resources?

3) Are there any trade-offs that could lead to other plans that would use all of these resources? If so, what are they?