Exercise 5.10. Consider the linear program minimize rER" subject to l

2 2. (10 pts) Consider the product XY where x and y are positive numbers which 2, must sum to six (6). Find the maximum value of xy under this contraint. a. Write the constraint equation. b. Use the equation in (a) to write the objective function in terms of the variable x. C. Apply the necessary calculus to solve the problem. Be sure to include a verification step, i.e. why your solution is the maximum. Also, give the maximum value.

[3.27] Consider the following problem: Maximize 2x₁ subject to X1 2x1 X1 X1, + x2 + 2x₂ + 3x2 x2, + 6x3 + 4x3 + x3 X3 X3, 11+ + 4x4 ********* X4 X4 ≤6 < 12 2 ≤ X4 X4 2 0.

3. Let u(x,y) = min (3x, 5y), p_x = 2, p_y = 5, and I = 20. Solve the constrained utility maximization problem, find x*, y*, and u*. Show it on the graph.