Is it True or False? For a maximization problem, we know that we have reached optimality when all the coefficients in the z row of the simplex table are positive
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Is it True or False?
For a maximization problem, we know that we have reached optimality when all the coefficients in the z row of the simplex table are positive..
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- TRUE OR FALSE In the simplex minimization method, optimality is signaled by the presence of all positive values in the Cj-Zj rowTRUE OR FALSE In the simplex maximization method, optimality is signaled by the presence of all negative values in the Cj-ZjInnis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…
- 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?A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solutionWhich of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.
- Dickie Hustler has $2 and is going to toss an unfair coin(probability .4 of heads) three times. Before each toss, hecan bet any amount of money (up to what he now has). Ifheads comes up, Dickie wins the number of dollars he bets;if tails comes up, he loses the number of dollars he bets.Use dynamic programming to determine a strategy thatmaximizes Dickie’s probability of having at least $5 afterthe third coin toss.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.Player A and B play a game in which each has three coins, a 5p, 10p and a 20p. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, then A wins B’s coin. But, if the sum is even, then B wins A’s coin. Find the best strategy for each player and the values of the game.
- Do the following problems using either TreePlan A student is deciding which scholarships (out of two) to accept. The first scholarship is worth $10,000 but carries the condition that recipients cannot accept another other forms of income (such as other scholarships). The second scholarship is awarded in a competition, where this student has a 50% chance of earning $7,000, a 40% chance of earning $10,000, and a 10% chance of earning $15,000. The student must inform the administrator of the first scholarship whether she will be accepting their offer today. A. Develop a decision tree to determine which scholarship this student should accept (using our normal decision criteria). B. Under what circumstance might the student accept the other scholarship?Find the dual of the problem. Please use excel to solve the problem. Thank you!a. What is the orrect graph that shows the feasible region for the problem. b. What are the extreme points of the feasible region? c. What is the correct graph that shows the optimal solution for the problem