Vladimir Pushkin, who frequently visits the US, can bring back a limited number of consumer items. The items, which he carries in a small bag, cannot exceed a weight of 25 Kilograms (25,000 grams). Once home, Vlad sells his booty at highly inflated prices. His four most popular items are denim jeans, silk shirts, tablet pcs, and tablet pc accessories. If he brings any tablet pcs, he needs to bring back at least twice that many accessories. About half of his customers who purchase jeans want silk shirts with their jeans so Vlad needs to satisfy this demand. Finally, Russian customs gets suspicious if a traveler brings in too many of electronic products, so Vlad limits the number of tablets he carries to three. The weight (in grams) and profit (in Rubles) of these items are shown in the table here: Jeans 1,000 grams 2,000 rubles Silk Shirts 500 grams 2,500 rubles Tablets 1,500 grams 4,000 rubles Accessories 250 grams 750 rubles Formulate an integer program for Vlad that will select a mix of items for him to take home that will maximize his profits. Be sure to define your decision variables and label your constraints. Clearly define your variables, provide your objective function and constraints using your variables (not in words). What is the optimal mix of items to carry? What is the optimal profit?