For Exercises 1 through 5, construct an equivalent essentially noncontracting grammar GL with a nonrecursive start symbol. Give a regular expression for the language of each grammar. 1. G:S--aS bSIB B -- bb I C X C-- cC 'k 2. G:S-ABCIX A - aA a B -- bB A C-- cC IX
Discuss the importance of combinatorial reasoning in gene sequencing and related problems involving genomes. Each writing assignment is worth 20 points should include the following sections : Background (3 points): This is a discussion of how the non -? mathematical and mathematical portions of your topic fit together. You migh t include a historical background of the topic, definitions of terms , the discrete mathematics ideas that are addressed (e.g. induction, logical fallacy, etc. ), and some explan ation about why these ideas were useful. Examples (10 points): In most of your writing assignments you are asked to discuss and describe an aspect of discrete mathematics. Give two of three examples or techniques of the topic under discussion. Give general information and also specific examples of the topic. Bibliography (2 points): List the references you used to complete this rep ort. J ust list title and author for any books and articles you used. You should also include a list of people that you consulted or any other form of help that you received. For example, you might obtain some of your information from the internet; in this case, you could include the website. You'll need at least one book or article as a reference, preferably two , and a total of at least two references. You'll notice that there are still 5 points unaccounted for. The remaining 5 points are for style: clarity, neatness, flow, design, organization and creativity -?-? it's important to be able to communicate your ideas.
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1. The weekly sales of Honolulu Red Oranges is given by q = 1116 ? 18p. Calculate the price elasticity of demand when the price is $31 per orange (yes, $31 per orange). Elasticity = ______ Interpret your answer. The demand is going down by ______% per 1% increase in price at that price level. Also, calculate the price that gives a maximum weekly revenue. $_________ Find this maximum revenue. $_______ 2. The consumer demand equation for tissues is given by q = (96 ? p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E when the price is set at $31. (Round your answer to three decimal places.) E = ___________ (b) At what price should tissues be sold in order to maximize the revenue? (Round your answer to the nearest cent.) $____________ (c) Approximately how many cases of tissues would be demanded at that price? (Round your answer to the nearest whole number.) _________ cases per week 3. The Physics Club sells E = mc2 T-shirts at the local flea market. Unfortunately, the club's previous administration has been losing money for years, so you decide to do an analysis of the sales. A quadratic regression based on old sales data reveals the following demand equation for the T-shirts: q = ?2p2 + 30p (9 ? p ? 15). Here, p is the price the club charges per T-shirt, and q is the number it can sell each day at the flea market. (a) Obtain a formula for the price elasticity of demand for E = mc2 T-shirts. E = ____________ (b) Compute the elasticity of demand if the price is set at $9 per shirt. (Round your answer to two decimal places.) Interpret the result. The demand for E = mc2 T-shirts is going down by about _______% per 1% increase in the price. 4. You have been hired as a marketing consultant to Big Book Publishing, Inc., and you have been approached to determine the best selling price for the hit calculus text by Whiner and Istanbul entitled Fun with Derivatives. You decide to make life easy and assume that the demand equation for Fun with Derivatives has the linear formq = mp + b, where p is the price per book, q is the demand in annual sales, and m and b are certain constants you must determine. (a) Your market studies reveal the following sales figures: when the price is set at $51.00 per book, the sales amount to 10,000 per year; when the price is set at $75.00 per book, the sales drop to 1000 per year. Use these data to calculate the demand equation. q = ________ (b) Now estimate the unit price that maximizes annual revenue. $_________ Predict what Big Book Publishing, Inc.'s annual revenue will be at that price. $________
