2 Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm:Z = 1X₁ + 1X₂MaximizeSubject to:2X₁ + 1X₂ ≤ 1001X₁ + 2X₂ ≤ 100X₁, X₂ ≥0Use computer software to solve the LP model.The optimum solution is:X₁ =stays the samechanges(C₁)(C₂)(round your response to two decimal places).(round your response to two decimal places).X₂ =Optimal solution value Z =(round your response to two decimal places).b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3, due to this change, theoptimal solution (1)(Use sensitivity table to answer this question.)c) If the impact of technical breakthrough was incorrectly determined and instead of X₁ profit coefficientincreasing to $3 it only increases to $1.25. As a result of this correction, the optimal solution found originally(Use sensitivity table to answer this question.)(2)changesstays the same120-110-100-90-80-70-60-50-40-30-20-10-C1Isoprofit LineC₂0-0 10 20 30 40 50 60 70 80 90 100 110 120+8xX1

Objective Functions and Constraints: Based on the given details, the objective…

Answered: Consider the following LP problem…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.3: The Exponential Distribution

Problem 3P

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Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60
Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
The annual demand for Prizdol, a prescription drug manufactured and marketed by the NuFeel Company, is normally distributed with mean 50,000 and standard deviation 12,000. Assume that demand during each of the next 10 years is an independent random number from this distribution. NuFeel needs to determine how large a Prizdol plant to build to maximize its expected profit over the next 10 years. If the company builds a plant that can produce x units of Prizdol per year, it will cost 16 for each of these x units. NuFeel will produce only the amount demanded each year, and each unit of Prizdol produced will sell for 3.70. Each unit of Prizdol produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. a. Among the capacity levels of 30,000, 35,000, 40,000, 45,000, 50,000, 55,000, and 60,000 units per year, which level maximizes expected profit? Use simulation to answer this question. b. Using the capacity from your answer to part a, NuFeel can be 95% certain that actual profit for the 10-year period will be between what two values?
A tire factory wants to set a minimum mileage guarantee on its tyre. Tyre tests reveals that the mean mileage has a normal distribution with mean 128 and standard deviation 1.76. the manufacturer wants to set the minimum guaranteed mileage so that no more than 2.5 percent of tyres will have to be replaced. The Lower limit of guaranteed mileage is :? (Write your answer in 2 decimals places)
Martin owns an older home, which requires minor renovations. However, the neighborhood where Martin lives mostly includes newly constructed luxury homes. Why might Martin's home increase in value? Based on the principle of substitution, the value of Martin's house will equal the value of the newly constructed homes in the neighborhood. ○ The value of Martin's home will decrease due to the new competition in the neighborhood. Based on the principle of regression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood. Based on the principle of progression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood.
Suppose that Pizza King and Noble Greek stopadvertising but must determine the price they will chargefor each pizza sold. Pizza King believes that Noble Greek’sprice is a random variable D having the following massfunction: P(D $6) .25, P(D $8) .50, P(D $10) .25. If Pizza King charges a price p1 and NobleGreek charges a price p2, Pizza King will sell 10025( p2 p1) pizzas. It costs Pizza King $4 to make a pizza.Pizza King is considering charging $5, $6, $7, $8, or $9 fora pizza. Use each decision criterion of this section todetermine the price that Pizza King should charge.
A college student works in both the school cafeteria and library. She works no more than 12 hours per week at the cafeteria, and no more than 16 hours per week at the library. She must work at least 20 hours each week. Write a system of inequalities that describes all the given conditions. Write a system of inequalities letting x= number of hours worked at the cafeteria per week and y = number of hours worked at the library per week. x+yz x≤ ys
Yearly oil production in Mexico, and yearly oil imports of the US from Mexico can be represented by the functions: P(t) = 3.0 – 0.13t million barrels I(t) 1.4 + 0.06t million barrels in year t, where t is the time in years since the start of 2000. a) What is represented by the functions P(t) – I(t) and I(t)/P(t)? What are the units for these functions? b) Let q(t) = I(t)/P(t). Compute q'(t) and q'(3). Interpret in a complete sentence. c) In marginal analysis, we would use q' (3) to estimate what quantity? Compute the actual value of that quantity and compare it with q'(3).
No probabilities are known for the occurrence of the nature states. Compare the solutions obtained by each of the following criteria: Maximin (Minimax)
Solve the following linear programming problem. Maximize: z=6x + 14y subject to: 7x+3y ≤21 9x+y≤21 x20, y 20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=
Which of the following statements is NOT true? Your answer: O Primal Simplex Algorithm starts feasible but nonoptimal O Dual Simplex Algorithm starts optimal but infeasible Generalized Simplex Algorithm starts optimal and infeasible

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