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2. (18%) Bob is given 30 dollars, and nothing else, to allocate between his consumptions of goods 1 and 2. The price of good 1 is equal to $5, and the price of good 2, $3. Denote x1 for his consumption quantity of good 1, and 2 that of good 2. a. The equation representing Bob's budget line is -_; the slope of the budget line is equal to Graph the budget line on the graph paper (and label the coordinates of the horizontal and vertical intercepts). b. Given each of the following utility functions for Bob, do the following: . draw the indifference curve corresponding to the utility level equal to 5, and the indifference curve corresponding to the utility level equal to 10 (be sure to label the coordinates of some points on the graph to leave no ambiguity about the position of each curve); . Given Bob's budget constraint, fill in the following blanks. i. If Bob's utility function is u(1, X2) := 10x1 + 5x2 for all 21, 22 2 0, Then the optimal bundle is: *1 = , 2 ii. If Bob's utility function is u(1, T2) := min{10x1, 52} for all 21, X2 2 0, Then the optimal bundle is: $1 =- -; 22 = iii. If Bob's utility function is u(1, X2) := max {10x1, 5x2} for all x1, 22 2 0, Then the optimal bundle is: $1 =- iv. If Bob's utility function is u(1, X2) := x] + x2 for all X1, X2 2 0, Then the optimal bundle is: 21 = -; 22 = c. Fill in the blanks: i. The Lagrange method with equality constraints is (applicable, inap- plicable) to Case (b.i) because according to the utility function in (b.i) (any, some) boundary point of the domain R4 is (more preferred, less preferred) than (any, some) interior point of R? ii. The Lagrange method with equality constraints is (applicable, inap- plicable) to Case (b.iii) because the utility function (satisfies, does not satisfy) the condition of (differentiability, strong monotonicity)