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Fruit Computer Company is ready to make its annual purchase of computer chips. Fruit can purchase chips (in lots of 100) from three suppliers. Each chip is rated as being of excellent, good, or mediocre quality. During the coming year, Fruit will need 5,000 excellent chips, 3,000 good chips, and 1,000 mediocre chips. The characteristics of the chips purchased from each supplier are shown in Table 57. Each year, Fruit has budgeted $28,000 to spend on chips. If Fruit does not obtain enough chips of a given quality, then the company may special-order additional chips at$10 per excellent chip, $6 per good chip, and$4 per mediocre chip. Fruit assesses a penalty of $1 for each dollar by which the amount paid to suppliers 1–3 exceeds the annual budget. Formulate and solve an LP to help Fruit minimize the penalty associated with meeting the annual chip requirements. Also use preemptive goal programming to determine a purchasing strategy. Let the budget constraint have the highest priority, followed in order by the restrictions on excellent, good, and mediocre chips. TABLE 57:

 Characteristics of a Lot of 100 Chips  Price Per 100 Chips ($)SupplierExcellentGoodMediocre 160202040025035153003402040250\begin{matrix} \text{ } & \text{Characteristics of a Lot of 100 Chips} & \text{ } & \text{ } & \text{Price Per 100 Chips (\$)}\\ \text{Supplier} & \text{Excellent} & \text{Good} & \text{Mediocre} & \text{ }\\ \text{1} & \text{60} & \text{20} & \text{20} & \text{400}\\ \text{2} & \text{50} & \text{35} & \text{15} & \text{300}\\ \text{3} & \text{40} & \text{20} & \text{40} & \text{250}\\ \end{matrix}

(Stock Market) Write a program to help a local stock trading company automate its systems. The company invests only in the stock market. At the end of each trading day, the company would like to generate and post the listing of its stocks so that investors can see how their holdings performed that day. We assume that the company invests in, say, 10 different stocks. The desired output is to produce two listings, one sorted by stock symbol and another sorted by percent gain from highest to lowest. The input data is provided in a file in the following format: symbol openingPrice closingPrice todayHigh todayLow prevClose volume For example, the sample data is:

MSMT 112.50 115.75 116.50 111.75 113.50 6723823 CBA 67.50 75.50 78.75 67.50 65.75 378233 . . . The first line indicates that the stock symbol is MSMT, today’s opening price was 112.50, the closing price was 115.75, today’s high price was 116.50, today’s low price was 111.75, yesterday’s closing price was 113.50, and the number of shares currently being held is 6723823. The listing sorted by stock symbols must be of the following form:

******************* First Investor's Heaven ********************
********************** Financial Report ************************
Stock                Today                        Previous     Percent
Symbol     Open     Close       High     Low      Close        Gain     Volume
------ ----- ----- ----- ----- -------- ------- ------
ABC       123.45    130.95     132.00   125.00  120.50        8.67%      10000
AOLK       80.00     75.00      82.00    74.00   83.00       -9.64%       5000
CSCO      100.00    102.00     105.00    98.00  101.00        0.99%      25000
IBD        68.00     71.00      72.00    67.00   75.00       -5.33%      15000
MSET      120.00    140.00     145.00   140.00  115.00       21.74%      30920
Closing Assets: $9628300.00

Develop this programming exercise in two steps. In the first step (part a), design and implement a stock object. In the second step (part b), design and implement an object to maintain a list of stocks. (Stock Object) Design and implement the stock object. Call the class that captures the various characteristics of a stock object stockType. The main components of a stock are the stock symbol, stock price, and number of shares. Moreover, we need to output the opening price, closing price, high price, low price, previous price, and the percent gain/loss for the day. These are also all the characteristics of a stock. Therefore, the stock object should store all this information. Perform the following operations on each stock object: i. Set the stock information. ii. Print the stock information. iii. Show the different prices. iv. Calculate and print the percent gain/loss. v. Show the number of shares. a.1. The natural ordering of the stock list is by stock symbol. Overload the relational operators to compare two stock objects by their symbols. a.2. Overload the insertion operator, <<, for easy output. a.3. Because the data is stored in a file, overload the stream extraction operator, >>, for easy input. For example, suppose infile is an ifstream object and the input file was opened using the object infile. Further suppose that myStock is a stock object. Then, the statement infile >> myStock; reads the data from the input file and stores it in the object myStock. (Note that this statement reads and stores the data in the relevant components of myStock.)


Cassie and Cliff decided that their company would specialize in designing Web logs, or "blogs." Since production of any blog requires about the same amount of programming time, each customer could be charged the same price. Cassie and Cliff also estimated that the number of customers in a year would be related to the price. by n(x) = 600 - 2x, where x is the price charged per blog. Production of each blog will require about $200 in programmer labor. To get started in business, they bought a computer for$2,000. (a.) Write rules for the following functions, simplifying where possible. i. Annual income from blog designs I(x) if the price is x dollars per blog. ii. Annual production costs for blog designs C(x) if the price is x dollars per blog. iii. Annual profit from the business P(x) if the price is x dollars per biog. iv. Profit per customer Pc(x)P_{c}(x) if the price is x dollars per blog. (b.) What would be reasonable domains for the functions in Part a? (c.) For what blog prices would the following functions be maximized? i. Income I(x). ii. Profit P(x). iii. Profit per customer Pc(x)P_{\mathrm{c}}(x) (d.) What price would you recommend that Cassie and Cliff charge per blog? Explain your reasoning.


Answered 2 years ago
Answered 2 years ago
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a. i. The income is given by the product of the number of customers and the price. This can be written as follows:

I(x)=x(6002x)=600x2x2\begin{aligned} I(x)&=x(600-2x)\\ &=600x-2x^2 \end{aligned}

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