1. Recall the Soylent Diet Planning problem discussed in class: In the distant future, spacefaring humans meet their nutritionary requirements by consuming Soylent brand Nutri-Paste in any of several varieties. One of the children has developed a deliciousness index for each variety. He wants to mix the varieties to create the average- tastiest meal that satisfies his mother's strict requirements: at least 1500 kCalories, no more than 20g of fat, and at least 100 g of protein, with a volume of exactly 30 ccs. Deliciousness kCal/cc Fat g/cc Protein g/cc Variety Soylent Blue 0.1 25 0.1 6.3 Soylent Red 0.25 110 2.2 1.8 Soylent Yellow 0.2 72 0.65 4.1 The starship makes it to port with all hands accounted for; they are surprised to find a new variety of Soylent available. Soylent green has 200 calories and 5 grams of protein but only .4 grams of fat per cubic centimeter. Surprisingly, it is the most palatable variety yet with a deliciousness index of 0.4! (a) Adapt the model given in class (or formulate your own) to include the new Soylent variety. (b) Suppose that Soylent green comes in individually packaged 4 cc blocks rather than a paste. How should this change the model? Write out the new model.