Problem 3 (10 pt): Assume that there are two engines in a rocket. which work as accelerator and stabilizer. with outputs a, 3). Let 1:, y be two parameters in the controller of the rocket. The speed is given by 20 31:2 + 21:3; - 81: + {a glyz. However' according to the safety issue. we must satisfy 3.1". + y S b. (8) Initially, the two engines are of the same type. with the same output a. : b : 8. Compute the maximal speed of the rocket. (You can assume that the Kuhn-Tucker Theorem already applies.) (b) One plan is to upgrade the first engine to slightly increase its output. Compute the rate of change of the maximal speed with respect to this increasing. (0) The other plan is to upgrade the second engine to slightly increase its output. Compute the rate of change of the maximal speed with respect to this increasing. ((1) If your budget only supports one upgrading. which engine will you choose