Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 3x + 22y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 (x,y)= f=
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Use the simplex method to maximize the given function. Assume all variables are nonnegative.
Maximize
subject to
| 14x | + | 7y | ≤ | 35 |
| 5x | + | 5y | ≤ | 50 |
(x,y)=
f=
Step by step
Solved in 2 steps
- Use the RAND function and the Copy command to generate 100 random numbers. a. What fraction of the random numbers are smaller than 0.5? b. What fraction of the time is a random number less than 0.5 followed by a random number greater than 0.5? c. What fraction of the random numbers are larger than 0.8? d. Freeze these random numbers. However, instead of pasting them over the original random numbers, paste them onto a new range. Then press the F9 recalculate key. The original random numbers should change, but the pasted copy should remain the same.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 60Can the function f (x) = - x2 + 3x +2 be maximized?
- Which of the following is/are linear function(s) of x, y, z? 2x A. y B. TTX + ey = 3z y- 3z C. 3x2 Select one: None A B. A and C All A and B B and CSTAR 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: 3Q) The sin() function can be evaluated by the following infinite series: x3 sin x = x - 3! 5! Create an M-file to implement this formula so that it computed and displays the values of sin(x) as each term in the series is added up to fifteenth order. For each step, compute and display the percent relative error as following: true – series approximation %error x 100% true
- 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.)Bad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.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
- Consider an ARIMA(2,1,1) process. Write out the resulting model usinga. Backshift notation with the backshift operator B.b. Backshift notation with the operatorc. No backshift notationUse the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 7x + 8y subject to x + 2y ≤ 10 x + y ≤ 7 (x,y)= f=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.