Name: ___________________________________________________________

1. Assuming that the computer uses 2 decimal digits, compute the range of a + b * c, where a is in the interval [0.9, 1.1], b is in the interval [0.009, 0.011], and c is in the interval [10, 16], with appropriate round-offs.

2-4. Estimate the range of function (1 - x) * (2 + x) on the interval [-3, 0] by using the following methods:

- use the centered form;
- use the mean valued form;
- use affine arithmetic.

5. A decision maker has three alternatives:

- for
the first alternative a
_{1}, the range of possible benefits is [10.0, 20.0]; - for
the second alternative a
_{2}, the range of possible benefits is [0.0, 30.0]; - for
the third alternative a
_{3}, the range of possible benefits is [-5.0, 30.0].

- a pessimist, for whom α = 0;
- an optimist, for whom α = 1;
- a decision maker for whom α = 0.5.

6. Use the interval-based optimization algorithm
to locate the maximum of the function
f(x) = x - x^{2} on the interval [0, 0.8]. Divide this
interval into two, then divide the remaining intervals into two
again, etc. Stop when you get intervals of width 0.1.

7-8. Use the constraints method to solve the following two problems:

- find x
_{1}and x_{2}, both from the interval [-10, 10], that satisfy the system of equations x_{1}+ x_{2}= 0 and x_{1}* (1 + x_{2}) = 0.09; - find x
_{1}and x_{2}, both from the interval [-10, 10], that satisfy the system of equations x_{1}+ x_{2}= 0 and x_{1}* (1 + x_{2}) = 10.

9. Briefly describe the topic of your class project and what you have done so far.