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- 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?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.An urn contains 10 red balls and 30 blue balls.a Suppose you draw 4 balls from the urn. Let Xi bethe number of red balls drawn on the ith ball (Xi 0 or1). After each ball is drawn, it is put back into the urn. Are the random variables X1, X2, X3, and X4 indepen-dent random variables? b Repeat part (a) for the case in which the balls are notput back in the urn after being drawn.
- STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 31. A certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. Determine the optimal exposure times for beam 1 and beam 2. The data for the radiation therapy is given below: Fraction of dose absorbed per second Average dosage Area Beam 1 Beam 2 (in kilorads) Brain 0.4 0.5 Spine 0.3 0.1 At most 2.7 Tumor 0.5 0.5 At most 6 Center of Tumor 0.6 0.4 At least 6 1 Add file4. Explain how the logit model overcomes the problems associated with the Linera Probability Model in binary dependent variaraile model.
- The members of a private golf club have handicaps that are normally distributedwith mean 15 and standard deviation 3.5. In a particular event, foursomes are chosen by grouping four players chosen at random from the club. The handicap of thefoursome is the arithmetic average of the handicaps of the four players comprisingthe foursome. In what proportion of the foursomes will the handicap of the foursome be less than 10 or more than 20? (Hint: The standard deviation of the average of four independent identically distributed random variables is exactly half thestandard deviation of one of them.)"A chipboard company has 4 factories, Mazatenango, Retalhuleu, Escuintla and Xela. It has four major distributors of its chipboards, which are distributor 1, distributor 2, distributor 3 and distributor 4: Mazatenango Retalhuleu Escuintla Xela DEMAND D1 10 16 19 12 350 D2 12 10 18 15 300 D3 15 22 10 10 250 IN THIS CASE USE VOGEL'S APPROXIMATION METHOD D4 20 10 12 20 200 SUPPLY 150 150 350 250 1) Formulate the problem as a transportation problem, solve it with the three methods and find the optimal cost for this problem. methods and find the optimal cost for this transportation problem. (remember to go through all possible routes).a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculato
- 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.Explain why the reward for a saddle point must be thesmallest number in its row and the largest number in itscolumn. Suppose a reward is the smallest in its row and thelargest in its column. Must that reward yield a saddle point?Suppose 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.