Small Business Management Entrepreneurship And Beyond 4th Edition Timothy S. Hatten - Solutions

Discover the ultimate resource for "Small Business Management: Entrepreneurship and Beyond, 4th Edition" by Timothy S. Hatten. Access an extensive online collection of answers key and solution manuals, offering step-by-step answers to all your textbook questions. Whether you're seeking solved problems or chapter solutions, our comprehensive test bank and instructor manual provide the guidance you need. Enhance your understanding with questions and answers available in an easy-to-navigate solutions PDF. Best of all, explore these invaluable resources with the convenience of a free download. Unlock the potential of your studies today!

Consider the matrix H = I —hhT, where h is a column vector in M.n and I is the properly sized identity matrix. Prove that H is orthogonal, provided that h T h = 1. This matrix is known as the Householder matrix.
Unlike usual algebra, in matrix algebra we may have AX though A^BandX/0 . Check with BX, even 1 0 2 0 1 1 2 0 2 B =1 3 0 4 2 3 0- 1 0x =6 5 7 2 2 4 3 3 6
Let A e Rm'n, and let D be a diagonal matrix in W""n. Prove that the product AD is obtained by multiplying each element in a row of A by the corresponding element in the diagonal of D. Check with A = D =2 0 0 0 - 3 0 0 0 7
Prove that the representation of a vector using a basis is unique.
Express the derivative of polynomials as a linear mapping using a matrix.
Solve the system of linear equations:xi + 2x2 - X3 — - 3 ari + 4x3 = 9 2ar2 + ar3 = 0 using both Gaussian elimination and Cramer's rule.
Prove the result of Eq. (9.40). You should use the result established in Problem 7.11 to find the expected value of X(n), given a sample of n independent observations from the uniform distribution on the interval [0,0].
Apply the method of maximum likelihood to estimate the parameters of a uniform distribution on the interval [a, b].
Consider an exponential distribution with rate λ. On the basis of a random sample of size n, apply the method of moments to estimate λ.
Consider a sequence of random variables 0 with probability 1 Xn n with probability —~n Does this sequence converge in probability to a number? What about convergence in quadratic mean?
Consider the simulation of a continuous review (Q, R) inventory control policy. Define the relevant events for the system, and outline a procedure for the management of each event. To deal with a specific case, assume that customers arrive according to a Poisson process and order a random amount of
Define an algorithm to generate pseudorandom variables characterized by the following density function:/(*) = 4 x - 1, if 1 < x < 2 3-x, if 2 < a; < 3 0, otherwise
A m-Erlang distribution with rate λ is obtained when summing m independent exponential random variables with rate λ. This distribution may be used to model more realistic random service times in queueing systems.Devise an efficient method to generate a sample of pseudorandom variables from the
Apply one-way ANOVA to check equality of means for the following sample:i = 1 82.31 160.98 230.84 522.06 449.25 t = 2 240.80 228.27 278.73 278.16 172.16 t = 3 181.55 188.83 334.07 326.81 327.55
In one-way ANOVA we define the sum of squares SS& and SS™. Prove the identity s s - = Σ Σ xij -nm*2- -SSb i j
In order to estimate the fraction of defective parts, you take a sample of size 1000 and find that 63 are not acceptable. Find a 99% confidence interval for the fraction of defective parts.
The following dataset is a random sample from a normal distribution:103.23, 111.00, 86.45, 105.17, 101.91 92.15, 97.40, 102.06, 121.47, 116.62 Find a 95% confidence interval for variance.
A study was done to measure the impact of fatigue on human performance when carrying out a certain task. The performance is measured by an appropriate index, the larger the better, which is measured at the beginning of the shift and after 3 hours of work. Ten workers are observed, resulting in the
You want to compare the reliability of two machines that insert chips onto electronic cards. The main problem is the occurrence of jams in the feeding mechanism, as this requires stopping production to fix the trouble. To this aim, you observe the number of jams when producing standard batches of
Air quality is measured by the concentration of a dangerous pollutant.The mayor of a city has engaged in a program to improve traffic conditions in order to decrease the concentration ofthat pollutant. Of course, there is a lot of day-to-day variability in measures. In the past, the average
TakeltEasy produces special shoes for runners, whose average life is 1250 km. In order to improve the product, they experiment with a new design, and test prototypes with a sample of 30 runners. The sample mean of product life is 1315 km, with a standard deviation of 70 km. Can we say that
In standard confidence intervals, you use the sample mean as an estimator of expected value. Now suppose that a friend of yours suggests the following alternative estimator:-^"= Τ7 ρ-^1 "t" TT-^2 + Χ-^3 + ρ-^4 + ' ' ' + ρ-^Ov-1 + η-^ΛΓ \ 2 2 2 2 2 2 where we assume that JV is an even
Find the 97% confidence interval, given a sample mean of 128.37, sample standard deviation of 37.3, and sample size of 50. What is the width of the confidence interval? Suppose that you want to cut the confidence interval by 50% (i.e., the new width should be half the previous one). How many
You have to compute a confidence interval for the expected value of a random variable. Using a standard procedure, you take a random sample of size N = 20, and the sample statistics are X = 13.38 and S = 4.58.• Compute a confidence interval at level 95%.• If you take additional observations,
The director of a Masters' program wants to assess the average IQ of her students. A sample of 18 students yields the following results:130, 122, 119, 142, 136, 127, 120, 152, 141 132, 127, 118, 150, 141, 133, 137, 129, 142• Build a 95% confidence interval for the average IQ.• Assuming that IQ
Consider two random variables X and Y, not necessarily independent.Prove that Cov(X -Y,X + Y)=0.
You have invested $10,000 in IFM stock shares and $20,000 in Peculiar Motors stock shares. Compute the one-day value at risk, at 95% level, assuming normally distributed daily returns. Daily volatility is 2% for IFM and 4%for Peculiar Motors, and their correlation is 0.68.
You are in charge of component inventory control. Your firm produces end items P\ and P2, which share a common component C. You need two components C for each piece of type P\ and three components for each piece of type P2· Over the next time period, demand is uncertain and modeled by a normal
You have to decide how much ice cream to buy in order to meet demand at two retail stores. Demand is modeled as follows:£>i = 100X + eu D2= 120X + e2 where X, e\, and ei are independent normal variables with expected value and variance given by (28,16), (200,100), (300,150), respectively. Random
Batteries produced by a company are known to be defective with a probability of 0.02. The company sells batteries in packages of eight and offers a money-back guarantee that at most one of them is defective. What is the probability that a package is returned? If a customer buys three packages, what
According to an accurate survey, 40% of people checked at the exit of a well-known pub have made excessive use of alcoholic drinks. If we take a random sample of 25 persons, what is the probability that at least 4 of them are flagged?
You are about to launch a new product on the market. If it is a success you will make $16 million; otherwise, you lose $5 million. The probability of success is 65%. You could increase chances of success by delaying product launch in order to improve product design; this would take 6 months and
Using the binomial expansion formula (2.3), prove that the PMF of the binomial distribution [see Eq. (6.16)] adds up to one.
Using Eq. (6.15), prove that the expected value of a geometric random variable X with parameter p is E[X] = 1/p. (Hint: Use the result in Example 2.40.)
Consider a generalization of the Bernoulli random variable, i.e., a variable taking values X\ with probability p and X2 with probability I—p. Which values of p maximize and minimize variance?
Consider the following extension of the EOQ model, often labeled economic manufacturing quantity (EMQ). Most of the assumptions of the EOQ and EMQ models are the same, but in the latter, rather than assuming instantaneous replenishment of inventory, inventory is replenished at production rate p,
Assume that you work from age 25 to age 65. At the end of each year, you contribute C to your pension fund, which is invested at a yearly rate r = 5%. At age 65 you retire and plan to consume $20,000 each year, until you die. Assuming that you die at age 85, and that interest rates remain constant,
Consider a stream of constant cash flows Ft= C, for t = 1,..., T.From Example 2.39, we know how to find its present value at time t = 0.Now imagine that these cash flows are the amount you invest to build your pension wealth; the current amount of wealth is invested at an interest rate r, which we
Prove that the intersection of two convex sets Si and S2 is a convex set.
Consider the following functions and tell if they are convex, concave, or neither:fi{x) = e'a+\ / 2 (x) = ln(x + l), / 3 (x) = x 3- x 2+ 2
In Example 2.33 we assume discrete-time compounding of interest. This results in the need for introducing modified duration, in Eq. (2.19), to get rid of an annoying factor 1 + y, where y is yield to maturity. Compute bond duration when assuming continuous-time compounding, at yield yc, and show
Consider function and find linear (first-order) and quadratic (second-order) approximations around points xo — 0 and xo = 10. Check the quality of approximations around these points.
Consider the following functions defined on piecewise domains:j-x, x0'h{x) = Ì3X, *>0 'h{x)~-3 2 In other cases, one should define an integral by considering the value of the function at the beginning of each time bucket. A notable case occurs in financial engineering models, where the so-called
Consider functions /(x) = x3— x and g(x) — x3+ x. Use derivatives to sketch the function graphs, and look for maxima and minima.
Find the first-order derivative of the following functions:
Find the equation of a line• With slope -3 and intercept 10• With slope 5 and passing through point (-2,4)• Passing through points (1,3) and (3,-5)
Find the domain of functions 1 1 f(x) = ,, —7> 9(x) y/l - x2- 1 ' Vx2+ 1 - x
Use the concepts that we have introduced in Chapter 2 to check the qualitative properties of the logistic function of Eq. (16.11).
Apply the formulas of multiple regression to the case of a single regressor, and verify that the familiar formulas for simple regression are obtained.
Prove the identity in Eq. (14.26)
Consider the fraction È of defective items in a batch of manufactured parts. Say that the prior distribution of È is a beta distribution with parameters «i = 5 and ct2 = 10 (see Section 7.6.2 for a description of the beta distribution). A new batch of 30 items is manufactured and two of them are
Consider again the Bayesian coin flipping experiment of Example 14.14, where the prior is uniform. If we use Eq. (14.21) to find the Bayesian estimator, what is the estimate of È after the first head? And after the second head?
Consider the data of the Braess' paradox example in Section 14.5, but imagine that a central planner can assign routes to drivers, in order to minimize total travel cost. Check that adding the new linke, as in Fig.14.4(b), cannot make the total cost worse.
Two firms have a production technology involving a fixed cost and constant marginal cost, as represented by the cost function:TCi(f t) = {f +C| * *« > 0 . i =1, 2 1^0 if
Two firms have the same production technology, represented by the cost function:T Cite ) = ^ + 2«·>» , «_i, S[0 if ft = 0 3 5 There is also an alternative way of interpreting Black-Litterman model in terms of robust"shrinkage" estimators; see, e.g., Chapter 9 of Ref. [8].The cost function
Consider the Cournot competition outcome of Eqs. (14.12) and (14.13).Analyze the sensitivity of the solution with respect to innovation in production technology, i.e., how a reduction in production cost c¿ for firm i affects equilibrium quantities, price, and profit.
Find the Nash equilibria in the games in Tables 14.2 and 14.4. Are they unique?
Consider a point-to-point transportation network consisting of M nodes. By "point-to-point" we mean that, given transportation requirements between all pair of nodes, there is a direct transportation link from each origin to each destination, without transshipment through intermediate nodes (this
Consider the plant location model of Section 12.4.5 [see Eqs. (12.54-12.55)]. Adapt the model to cope with uncertain demand scenarios, building a two-stage stochastic linear programming model with recourse.
We know that VaR, in general, is not a subadditive risk measure.Consider a portfolio of two assets, with jointly normal returns.• Show that, in this specific case, VaR is a subadditive risk measure.• Is standard deviation a subadditive measure in the case above? What can we say in general?
You have invested $150,000 in stock shares of Doom and $200,000 in stock shares of Mishap. Assume that daily returns follow a multivariate normal distribution; daily volatilities for the two stock shares are 2% and 3%, respectively, and correlation is 0.8. Find the one-day VaR at 99% confidence
An investor has an initial wealth WQ that must be allocated between a risk-free asset, with certain return r{, and a risky asset. We assume a simple binomial model of uncertainty, like we did in Section 3.1. The return of the risky asset will either be ρ u or R¿, with probabilities pu and p¿,
You own a plant whose value is $100,000. In case of a fire, the value of your property might be significantly reduced or even destroyed, depending on how severe the accident is. Let us represent risk by the following scenarios:Scenario Value ($) Probability 1 100,000 0.95 2 50,000 0.04 3 1 0.01 For
A decision maker with a quadratic utility function of the form (13.12)is offered the following lottery:Probability Payoff 0.20 $10,000 0.50 $50,000 0.30 $100,000 If the risk aversion coefficient is λ = 1/150,000:• What is the certainty equivalent of the lottery?• What is the risk premium?
You are the manager of a pension fund, and your fee depends on the return attained. You can play it safe and allocate wealth to a risk-free portfolio earning 4% per year. Alternatively, you can pursue an active portfolio management strategy, whose a return is normally distributed, with expected
The Research and Development (R&D) division of your firm has developed a new product that could be immediately launched on the market. If so, the probability of success is 60%, in which case profit has a present value of €10 million (discounting all future cash flows). In case of flop, you will
Consider again the "fancy coin flipping" example of Section 1.2.3, i.e., the decision of producing a movie or not. Formalize the problem with a proper decision tree.
A firm sells a perishable product, with a time window for sales limited to 1 month. The product is ordered once per month, and the delivery lead time is very small, so that the useful shelf life is really 1 month. Each piece is bought at €10 and its sold for €14; if the product expires, it can
Given the observed data x 45 50 55 60 65 70 75 y 24.2 25.0 23.3 22.0 21.5 20.6 19.8 build a 95% confidence interval for the slope.
Consider the following sales data:Week 12345678 9 10 Sales 30 20 45 35 30 60 40 50 45 65 Build a linear regression model to predict sales and calculate R2.
In some applications we are interested in the distribution of the maximum among a set of realization of random variables. Let us consider a set of n i.i.d. variables Ui, i = 1,... ,n, with uniform distribution on the unit interval [0,1]. Let X be their maximum: X = max{Ui, U2, ■ ■ ·, Un}.
You are in charge of deciding the purchased amount of an item with limited time window for sales and uncertain demand. The unit purchase cost is $10 per item, the selling price is $16, and unsold items at the end of the sales window have a salvage value of $7 per item. Demand is also influenced by
You work for a manufacturing firm producing items with a limited time window for sale. Items are sold by a distributor facing uncertain demand over the time window, which we model by a normal distribution with expected value 10,000 and standard deviation 2500. The distributor decides how many items
Let X ~ χ^ be a chi-square variable with n degrees of freedom. Prove that E[X] = n.
You have just issued a replenishment order to your supplier, which is not quite reliable. You have ordered 400 items, but what you will receive is a normal random variable with that expected value, and standard deviation 40 (let us assume that using a continuous random variable is a sensible
Let X be a normal random variable with expected value μ = 6 and standard deviation σ = 1. Consider random variable W = 3X2. Find the expected value E[W] and the probability P(W > 120).
A friend of yours is an analyst and is considering a probability model to capture uncertainty in monthly demand of an item featuring high-volume sales. He argues that the central limit applies and, after a thorough check of data, proposes a normal distribution with expected value 12,000 and
You are working in your office, and you would like to take a very short nap, say, 10 minutes. However, every now and then, your colleagues come to your office to ask you for some information; the interarrivai time of your colleagues is exponentially distributed with expected value 15 minutes. What
We should set the reorder point R for an item, whose demand during lead time is uncertain. We have a very rough model of uncertainty - the lead time demand is uniformly distributed between 5000 and 20000 pieces. Set the reorder point in such a way that the service level is 95%.
Consider a normal variable with μ = 250 and σ — 20, and find the probability that X falls in the interval between 230 and 260.
A random variable X has normal distribution with μ = 250 and σ = 40.Find the probability that X is larger than 200.
Professors at a rather unknown but large college have developed a habit of heavy drinking to forget about their students. The following data show the number of hangovers since the beginning of semester, disaggregated for male and female professors:N hangovers Gender 0 1 > 2 Male 61 23 40 Female 66
Management wants to investigate the time it takes to complete a manual assembly task. A sample of 12 workers is timed, yielding the following data(in seconds):21.3 15.2 13.6 16.1 15.0 19.2 21.0 14.3 15.6 20.1 21.1 22.2• Find mean and median; do you think that the data are skewed?• Find the
You observe the following data, reporting the number of daily emergency calls received by a firm providing immediate repair services for critical equipment:Day 1 2 3 4 5 6 7 8 N calls 5462382 4 Day 9 10 11 12 13 14 15 16 N calls 4235644 6• Compute mean, mode, and quartiles.• Find the cumulated
The following table shows a set of observed values and their frequencies:Value 1 2 3 4 5 6 7 8 Frequency 5 4 7 10 13 8 3 1• Compute mean, variance, and standard deviation.• Find the cumulated relative frequencies.
You are carrying out a research about how many pizzas are consumed by teenagers, in the age range from 13 to 17. A sample of 20 boys/girls in that age range is taken, and the number of pizzas eaten per month is given in the following table:4 12 7 11 9 7 8 13 16 11 4 7 5 7 11 7 7 41 9 14• Compute
Consider the optimal mix model of Section 1.1.2. How could we extend the model to cope with• Third-party suppliers offering items at given cost?• The possibility of overtime work at some resource centers?
Consider the optimal mix model of Section 1.1.2. How could we extend the model to cope with • Third-party suppliers offering items at given cost? • The possibility of overtime work at some resource centers?
Consider again the growth option problem of Section 1.2.2. We want to check the impact of less extreme assumptions about the conditional probabilities for the second movie, but we are unsure which values we should use. So, we assume that the conditional probability of a second success, after a
Identify the three main considerations in setting a price for a product.
Explain what breakeven analysis is and why it is important for pricing in a small business.
Present examples of customer-oriented and internal-oriented pricing.
Explain why and how small businesses extend credit.
Describe the advertising, personal selling, public relations, and sales-promotion tools that a small business owner uses to compile a promotional mix.
What strategies should be considered if a small business is setting prices for a product that is to be exported? How do these strategies differ from those used in a domestic market? LO-3
What advantages and disadvantages are involved for a small business offering sales on credit? LO-3
As the owner of a small, hometown drugstore, how would you prepare for a Wal-Mart being built in your area? LO-3
What can happen if the price of a product does not fit with the three other Ps of the marketing mix? LO-3
Should a small business owner’s judgment be used to determine prices if so many mathematical techniques have been developed for that purpose? LO-3
Discuss the importance of remaining professional and friendly when trying to collect an unpaid bill. LO-3

Showing 3400 - 3500 of 4673

First
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Last

Small Business Management Entrepreneurship And Beyond 4th Edition Timothy S. Hatten - Solutions

Step by Step Answers