FIGURE 4.28 in Software

Integrating Code 39 Extended in Software FIGURE 4.28

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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
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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.
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