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At the optimal solution to the linear programming problem described in part 3, how many of the requirements will be satisfied?

		At least one, but less than half of them
		None of them
		All of them
		At least half, but not all of them

In part 3, which of the following represents requirement iii? X5 0.1(X1+X2+X3+X4+X5+X6) X5 0.1(X1+X2+X3+X4+X5+X6) 0.1X5 X1+X2+X3+X4+X5+X6 0.1X5 X1+X2+X3+X4+X5+X6 In part 3, which of the following represents requirement v? X1 + X2 + X3 + X4 + X5 + X6 150 X1 150, X2 150, X3 150, X4 150, X5 150, and X6 150 X1 150, X2 150, X3 150, X4 150, X5 150, and X6 150 X1 + X2 + X3 + X4 + X5 + X6 150 In part 3, which of the following represents requirement ii? 0.25(X2+X3) X1+X2+X3+X4+X5+X6 X2+X3 0.25(X1+X2+X3+X4+X5+X6) 0.25(X2+X3) X1+X2+X3+X4+X5+X6 X2+X3 0.25(X1+X2+X3+X4+X5+X6) In part 3, what is the objective function? Maximize 60X1 + 90X2 + 100X3 + 80X4 + 140X5 + 15X6 Minimize 60X1 + 90X2 + 100X3 + 80X4 + 140X5 + 15X6 Minimize 0.25X1 + 0.30X2 + 0.50X3 + 0.60X4 + 0.15X5 + 0.40X6 Maximize 0.25X1 + 0.30X2 + 0.50X3 + 0.60X4 + 0.15X5 + 0.40X6 In part 3, which of the following represents requirement vi? X1 + X2 + X3 + X4 + X5 + X6 1000 2X1 + 3X2 + 4X3 + 3X4 + 6X5 + 3X6 1000 2X1 + 3X2 + 4X3 + 3X4 + 6X5 + 3X6 1000 X1 + X2 + X3 + X4 + X5 + X6 1000

Part 3 Carnations plans to hold a soft opening on a Friday night for a select group of diners. In this opening, they will seat tables of 10 people and serve each table a five-course meal. The final course is dessert, and management is currently working to determine what to serve for this course. The leading idea is to serve each table a dessert tray that contains many different dessert options. To simplify matters, only one type of tray will be prepared. TJ.'s current task is to determine what desserts will be on the tray and the quantity (measured in ounces) of each desert to be included on the tray. The options are ice cream cheesecake, chocolate cake, tiramisu, cookies, and fruit parfait. The below table shows, for each dessert, its cost per ounce, calories per ounce, and space required per ounce Management would like to create a dessert tray that satisfies the below requirements at minimum cost. i) The entire tray is to have no more than 6000 calories. At least 25% of the total tray (by weight) should be composed of a combination of cheesecake and chocolate cake. Cookies can be no more than 10% of the total offering (by weight). At least 20% of the tray should be in a combination of fruit parfait and ice cream. iv) v) vi) Each tray should weigh at least 150 ounces. The total space used should not exceed 1000 square inches Calories (per ounce) Cost (per ounce) Dessert Ice Cream Cheesecake Chocolate Cake Tiramisu Cookies Fruit Parfait 60 90 100 80 140 15 $0.25 $0.30 $0.50 $0.60 $0.15 $0.40 Space (square inches per ounce) 2 3 4 3 6 The decision variables for this problem, X1, X2, X3, X4, X5, and x6, denote the amount (in ounces) of ice cream, cheesecake, chocolate cake, tiramisu, cookies, and fruit parfait, respectively, to be included on the dessert tray. For example, X3 is the amount (in ounces) of chocolate cake to include on the tray- Part 3 Carnations plans to hold a soft opening on a Friday night for a select group of diners. In this opening, they will seat tables of 10 people and serve each table a five-course meal. The final course is dessert, and management is currently working to determine what to serve for this course. The leading idea is to serve each table a dessert tray that contains many different dessert options. To simplify matters, only one type of tray will be prepared. TJ.'s current task is to determine what desserts will be on the tray and the quantity (measured in ounces) of each desert to be included on the tray. The options are ice cream cheesecake, chocolate cake, tiramisu, cookies, and fruit parfait. The below table shows, for each dessert, its cost per ounce, calories per ounce, and space required per ounce Management would like to create a dessert tray that satisfies the below requirements at minimum cost. i) The entire tray is to have no more than 6000 calories. At least 25% of the total tray (by weight) should be composed of a combination of cheesecake and chocolate cake. Cookies can be no more than 10% of the total offering (by weight). At least 20% of the tray should be in a combination of fruit parfait and ice cream. iv) v) vi) Each tray should weigh at least 150 ounces. The total space used should not exceed 1000 square inches Calories (per ounce) Cost (per ounce) Dessert Ice Cream Cheesecake Chocolate Cake Tiramisu Cookies Fruit Parfait 60 90 100 80 140 15 $0.25 $0.30 $0.50 $0.60 $0.15 $0.40 Space (square inches per ounce) 2 3 4 3 6 The decision variables for this problem, X1, X2, X3, X4, X5, and x6, denote the amount (in ounces) of ice cream, cheesecake, chocolate cake, tiramisu, cookies, and fruit parfait, respectively, to be included on the dessert tray. For example, X3 is the amount (in ounces) of chocolate cake to include on the tray

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