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- Find the Ma X Z = Xit X2 optimal solution by the large M X+ X2 3• ---- S.to メ4 >1 (3) X2 < 2 14) X1 304. Explain how the logit model overcomes the problems associated with the Linera Probability Model in binary dependent variaraile model.1. Find the maximum and minimum value of the LPP using the given below: Objective Function, Z=15X, +1 50 10 30 20 10 x1 30 40 60 do 70 80 90 10 20
- 2 Vidhya Balan is planning to liquidate her investments inmutual funds and invest in real estate. Before makingthe change to her investment strategy, Vidhya wants toforecast the price of mutual funds for the next 2 months.She has collected the following data on the average fundprices for the past 10 months.Month Average Fund Price1 55.12 53.83 53.44 52.955 52.156 52.757 52.658 51.59 52.2510 51.7a Using a five-period moving average, forecast theaverage fund price for Period 11.b. Using exponential smoothing with α = 0.3 forecastthe average fund price for Period 11. Assume an initialforecast for Month 2 (F2) as 55.10Suppose 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.Minimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0
- Suppose your total benefits of renting x DVD's next month is: -²2² +14x+50 The cost of renting a DVD is $2, and so the total cost of renting x DVD's is $2x. Calculate your net benefit from watching 1, 2...8 DVDs. Complete column (2). (Enter your responses as integers.) (1) DVDs Rented 0 1 N345678 2 (2) Total Net BenefitSuppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2
- #17FAVORABLE UNFAVORABLEMARKET MARKETEQUIPMENT ( $) ($)Sub 100 300,000 –200,000Oiler J 250,000 –100,000Texan 75,000 –18,000For example, if Ken purchases a Sub 100 and ifthere is a favorable market, he will realize a profitof $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. ButKen has always been a very optimistic decisionmaker.(a) What type of decision is Ken facing?(b) What decision criterion should he use?(c) What alternative is best? #18Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob iscredited with making the company a financial success. Bob is vice president of finance. Bob attributeshis success to his pessimistic attitude about business and the oil industry. Given the information fromProblem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should Bobuse, and what alternative…Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O OA cement mix company is renowned for providing high strength concrete additives - at high unit cost. It delivers two types of cement additives - Tuf and Rok. In making these additives the company adds two special products, Qikcem and Plascem. These additives contain two (2) basic ingredients: Lime and Flyash, in different proportions, as shown in the table below. Flyash [%] Lime Cost Special Products Qikcem (1) Plascem (2) Availability [kg/hr] 2600 3600 [%] [S/kg] 10 15 45 55 35 65 The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at least 45% of Flyash. The company can sell at most 800oerkg of its additive products (Tuf and Rok) per hour. There are other limitations and local requirements, as stated beklew: a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be produced b) The plant has contracted to deliver at least 3500 kg/hour of Tuf c) The company is restricted, by local…