FIGURE 4.28 in Software

Integrating Code 39 Extended in Software FIGURE 4.28

413 414 415 500 501 502 503 504 505

We can easily nd y s that satisfy the inequalities on the right by simply making them large enough, for example (y1 , y2 , y3 ) = (5, 3, 6). But these particular multipliers would tell us that the optimum solution of the LP is at most 200 5 + 300 3 + 400 6 = 4300, a bound that is far too loose to be of interest. What we want is a bound that is as tight as possible, so we should minimize 200y1 + 300y2 + 400y3 subject to the preceding inequalities. And this is a new linear program! Therefore, nding the set of multipliers that gives the best upper bound on our original LP is tantamount to solving a new LP: min 200y1 + 300y2 + 400y3 y1 + y 3 1 y1 , y 2 , y 3 0 By design, any feasible value of this dual LP is an upper bound on the original primal LP. So if we somehow nd a pair of primal and dual feasible values that are equal, then they must both be optimal. Here is just such a pair: Primal : (x1 , x2 ) = (100, 300); Dual : (y1 , y2 , y3 ) = (0, 5, 1). y2 + y 3 6

0:10x 0:30 100 x 0:25 100 0:10x 30 0:30x 25 30 0:20x 25 30 30 0:20x 5 5 x 0:20 x 25

Input/output (I/O) addresses are simple in concept. Each device in a computer system needs a way to communicate. The early standard was to assign an area in memory designated for a particular device. This allowed for a simple method of communicating between devices. For example, the default I/O address for a joystick is 200h to 20Fh. This address range is used for communications between a joystick and the computer. Generally, no other device uses those addresses. Notice the h on the end of the address. The h signifies that this address is a hexadecimal address (base 16). Table 1-5 gives you the most commonly asked I/O addresses in the A+ exam. Make sure you memorize these addresses, as you can expect to be asked about one or more of them.

60 00

prior to expiration, the exerciser loses any premium value above the intrinsic value of the option.