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- 9. Consider the problem of minimizing x+2y subject to the constraint x+y=1. What is the optimal level of x and y? x=? y=? 10. Consider the problem of minimizing 3x+2y subject to the constraint x+y=1. What is the optimal level of x and y? x=? y=?Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 1212) Melquiades is worried about his grades from the microeconomics course, according to the rules for grading, the final grade is obtained as the minimum between the grade for the midterm test (x) and the final test (y). The utility function of Melquiades will depend on the grades obtained from those two tests Now, Melquiades has researched that the average student needs to study 24 minutes an additional point in each test (tests are graded from 0 to 100) obtain a) If Melquiades has 20 hours to study for both tests (x and y), how much time would he employ for each test? Figure out the grade that Melquiades will obtain in each test and his final grade in microeconomics. Elaborate a graph. b) How much additional study time would Melquiades require to increase his final grade by 10 points. Elaborate a graph. c) Suppose the difficulty of the final test increases in such a way that now each additional point would require 26 minutes of study. What would be the total cost (in minutes)…
- Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of cake accounts for at least 30% of the total production per day. What is the correct linear constraint to show this? Group of answer choices 0.3x – 0.7y – 0.7z ≥ 0 0.7x – 0.3y – 0.3z ≥ 0 0.7x – 0.3y – 0.7z ≥ 0 0.3x – 0.7y – 0.3z ≥ 0Economics Consider the following set of constraints (Maixmization problem): 22X+ 44Y>= 18, and 66X+ 22Y >= 9. The following is true for this problem: a. X= 0, Y 22 is the only optimal solution. O b. Infeasible problem. C. Unbounded problem. d. X-22, Y=-2 is the only optimal solution.The following scenario examines the relationship between marginal and average values. Suppose Lee is a high school basketball player. The following table presents their game-by-game results for foul shots. Fill in the columns with Lee's foul-shooting percentage for each game and their overall foul-shooting average after each game. Game Result Total Game Foul-Shooting Percentage Average Foul-Shooting Percentage Game 1 8/10 8/10 2 4/10 12/20 3 2/8 14/28 4 2/4 16/32 5 6/8 22/40 80 80 On the following graph, use the orange points (square symbol) to plot Lee's foul-shooting percentage for each game individually, and use the green points (triangle symbol) to plot Lee's overall average foul-shooting percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. FREE-THROW PERCENTAGE 100 90 80 70 60 50 40 30 20 10 0 0 2 3 GAME Game Foul-Shooting Percentage Average Foul-Shooting Percentage ? You can…
- Consider the problem: minf,(x, y) = x² +y² minf;(x, y) = y²= x + 5 st. -5 < x, y:<5 Solve by the constraint method: find only a few Pareto optimal: 2: solutionsLet say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of candy is at least equal to the total number of cake and bread. What is the correct linear constraint to show this? Group of answer choices z – x – y ≥ 0 x – 2y – z ≥ 0 y – x – z ≥ 0 x – y – z ≥ 0The following scenario examines the relationship between marginal and average values. Suppose Jelani is a high school basketball player. The following table presents their game-by-game results for foul shots. Fill in the columns with Jelani's foul-shooting percentage for each game and their overall foul-shooting average after each game. Game Result Total Game Foul-Shooting Percentage Average Foul-Shooting Percentage Game 1 8/10 80 2 14/20 3 15/25 4 18/30 5 26/40 FREE-THROW PERCENTAGE On the following graph, use the orange points (square symbol) to plot Jelani's foul-shooting percentage for each game individually, and use the green points (triangle symbol) to plot Jelani's overall average foul-shooting percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 100 90 80 70 60 50 40 30 20 10 0 8/10 6/10 1/5 3/5 8/10 0 2 GAME 3 80 4 5 Game Foul-Shooting Percentage Average Foul-Shooting…
- 4. Suppose Hank is shopping for a shirt, and the set of all possible alternatives consists of an American Eagle shirt, a Gap shirt, and a Hathaway shirt. (a) Using the notation from class, specify an example of a choice structure for the choice facing Hank that satisfies the Weak Axiom of Revealed Preference (WARP). Explain why it satisfies WARP. (b) Using the notation from class, specify an example of a choice structure for the choice facing Hank that violates the Weak Axiom of Revealed Preference (WARP). Explain why it violates WARP.A consumer has preferences over two goods, carrots and turnips, each measured in kilograms. For each of the following scenarios, identify which, if any, of the standard assumptions of preferences are violated. (a) The consumer will never eat more than ten kilograms of carrots per day. (b) The consumer cares only about the total weight of the two vegetables consumed, and always prefers more to less. (c) The consumer cares only about the product of the respective weights of the two vegetables consumed, and always prefers a greater product to a lesser one.14. What assumption is important in using economic model to make predicitons? a) the law of demand b) the rationality assumption c) ceteris paribus/ other things being equal d)evryone being a price taker