Determine the maximin and minimax strategies for the two-person, zero-sum matrix game. 45-1 The row player's maximin strategy is to play row The column player's minimax strategy is to play column
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- Use 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=Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 20x + 12y + 12z subject to the following. x + z ≤ 45 x + y ≤ 30 y + z ≤ 45 (x,y,z)= f=Solve the given standard minimization problem using duality. (You may already have seen some of these in earlier sections, but now you will be solving them using a different method.) HINT [See Example 1.] Minimize c = s + 2t subject to 4s + t ≥ 210 2s + t ≥ 160 s + 3t ≥ 315 s ≥ 0, t ≥ 0. c= (s, t) =
- Write a program that asks the user for an angle, entered in degrees. The program should then display the sine, cosine, and tangent of the angle. (Use the sin, cos, and tan library functions to determine these values.) You must convert the angle into radians (angle * 3.14/180)Consider the problem of calculating the median m of the following numbers: 4,5,9. (a) Write down the linear program that you could solve, to find the median m. Then put this LP in the form: min c^T x s.t. Ax ≥ b, x ≥ 0, where x is your list of variables. (b) Now write down the dual of the problem above. Call the list of dual variables y. (Hint: there are 6 components of y.)linear programming A small company works 10 hours a day, making two types of products from 3 specific processes. The times required in each of the processes and the profits generated by type of product are shown in the table: Product Process 1 Process 2 Process 3 Utility 1 10 6 8 $2.00 2 5 20 10 $3.00 consider that x1 and x2 are the quantities of the product 1 and 2. Indicate: Objective function Restriction of the process 1 Restriction of the process 2 Restriction of the process 3 Restriction of nonnegativity Optimal solution of x1, x2 and z
- In a study of how cheif excutive officers (CEOs) spend their days, it was foudn that CEOs spend an average of about 18 hours per week in meetings, not including conferance calls, business meals, and public events. Shown here are the times spent per week in meetings (hours) for a sample of 25 CEOs: 14, 15, 18, 23, 15, 19, 20, 13, 15, 23 23, 21, 15, 20, 21, 16, 15, 18, 18, 19 19, 22, 23, 21, 12 a. What is the least amount of time a CEO spent per week in meetings in this sample? The highest? b. Use a class width of 2 hours to prepare a frequency distribution and a percent frequencey distribution for the data. c. Prepare a histogram and comment on the shape of the distribution.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.Coefficient of the variables in the objective function occur in which row