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14.10 The distance by bus from New York to Boston is 225 miles. The bus driver gets paid $12.50 per hour, while the other costs of running the bus at a steady speed of x miles per hour amount to 90 + 0.5x cents per mile. The minimum and maximum legal speeds on the bus route are 40 and 55 miles per hour. At what steady speed should the bus be driven to minimize the total cost 14.11 A charter airline is planning a ight for which it is considering a price of between $150 and $300 per person. The airline estimates that the number of passengers taking the ight will be 200 0.5x, depending on the price of x dollars that will be set. What price will maximize the income 14.12 Suppose that a company can sell x radios per week if it charges 100 0.1x dollars per radio. Its production cost is 30x + 5000 dollars when x radios are produced per week. How many radios should be produced to maximize the pro t, and what will be the selling price per radio 14.13 A box with square base and vertical sides is to be made from 150 square feet of cardboard. What dimensions will provide the greatest volume if: (a) the box has a top surface; (b) the box has an open top 14.14 A farmer wishes to fence in a rectangular eld, and also to divide the eld in half by another fence (AB in Fig. 14-6). The outside fence costs $2 per foot, and the fence in the middle costs $3 per foot. If the farmer has $840 to spend, what dimensions will maximize the total area

The additional N K redundant symbols are derived from the message symbols but are not part of the message The number of possible codewords is 2N, but only 2K of these will contain datawords, and these are the ones that are transmitted It follows that the rest of the codewords are redundant, but only in the sense that they do not contribute to the message If errors occur in transmission, there is high probability that they will convert the permissible codewords into one or another of the redundant words that the decoder at the receiver is designed to recognize as an error It will be noted that the term high probability is used There is always the possibility, however remote, that enough errors occur to transform a transmitted codeword into another legitimate codeword even though this was not the one transmitted.

B.7.3 SIMPLE VARIABLES A variable is a named storage area to keep numbers or strings. Variable names must start with a letter but then any combination of letters and numbers can be used. Variable names are case sensitive, so Distance and distance a re different.

It will be observed that the wording of the preceding paragraph parallels that given in Sec 112 on block codes, except that here the coding is carried out on symbols Some of the design rules for the R-S codes are q N 2t 2 q N.

The length of a variable name can be up to 255 characters, so you can use names like DistanceToBeacon_1. It is important to use meaningful names in your programs because this makes your programs easier to read and understand. A variable can be used anywhere a number or string is used. As long as the variable has been assigned a value before using it, it can substitute for its value. A variable is assigned a value in an assignment statement (see Sec. B.3) or by passing it as a parameter to a command that will assign it a value. Unlike standard BASIC and many other programming languages, variables in RobotBASIC do not have to be prede ned as being of a speci c type. Any variable can store any value type ( oat, integer, or string). Additionally, you can reassign a value of a different type to a variable that already holds a certain type. If a variable exists when it is being assigned a value, it does not matter what the old value is or of what type it is, the new value will replace the old one. If the original value is an integer and the new value is a string the variable type will be changed to a string, and vice versa. The same is true for oats and integers and oats and strings. In certain operations RobotBASIC will convert between variable types as necessary if it can. For example, if you add an integer to a string the integer will be converted to its string representation and concatenated to the string. If the operation cannot be performed the system will return an error. For example:

Fig. 14-6

Here, t is the number of symbol errors that can be corrected. A simple example will be given to illustrate these. Let k 2; then q 4, and these four symbols may be labeled A, B, C, and D. In terms of the binary symbols (bits) for this simple case, we could have A 00, B 01, C 10, and D 11. One could imagine the binary numbers 00, 01, 10, and 11 being stored in memory locations labeled A, B, C, and D. The number of symbols per codeword is N q 1 3. Suppose that t 1; then the rule 2t N K gives K 1; that is, there will be one symbol per dataword. Hence the number of datawords is qK 4 (i.e., A, B, C, or D), and the number of codewords is qN 43 64. These will include permissible words of the form AP1P2, BP3P4, CP5P6, and DP7P8,