When using the simplex algorithm, an error was made in choosing the pivot row. Which of the following will be the result of this? The solution in the next tableau will: a. have a worse objective value b. be nonbasic c. be infeasible d. be unaffected
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A: Slack variable:A variable added to the problem to eliminate less-than constraints.
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- a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution? b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithm.A linear programming problem has objective function P = 3x+2y and the following linear inequality constraints below. How many slack variables are needed for the simplex algorithm? What is the correct way to arrange this equation in order to enter it into a Simplex Tableau?Use the dual simplex algorithm in order to find a solution if the constraint x1 <= 2 is added
- Assemble the Linear Programming problem from the SIMPLEX table:Recreate the LINEAR PROGRAMMING PROBLEM based on the image of the LP MODEL attached belowUse the simplex algorithm to solve the following linear optimisation problem: maximisef(x1,x2,x3)=3x1+x2+2x3 subjectto: 3x1 +2x2 +x3 ≤8 x1 +2x2 +2x3 ≤4, x1,x2,x3 ≥0. You must address each of the 5 steps of the algorithm as presented in the course notes and videos in your answer.
- Use the simplex algorithm to solve the following problem (Use tableaus)Consider the following primal problem and its dual, which of the following is the optimal solution?An entrepreneur is deciding how to subdivide a large old home toconvert it to a Bed-and-Breakfast (B&B). There are four alternatives: OptionA renovates all rooms, but leaves all walls intact, so the result would be twodouble rooms and three single rooms on the top floor, and on the main floor two further single rooms with a shared bathroom. Option B would renovate only the second floor but combine the single rooms in the main floor to create a single room with a bathroom. Option C combines the main floor rooms to create a single room with a bathroom, and combines the three single rooms on the top floor to create two double rooms. Finally option D would create five double rooms, each with its own bathroom. There are three event possibilities, a high demand, an average demand, and a low demand. The entrepreneur believes the probability of each event depends on the layout and availability of the rooms. Below are the details of the predicted income and the probability of occurrence…
- Show that the linear programming problem is unbounded.At Long John Silver’s (LJS), Platter 1 comes with 2 pieces of fish, 3 pieces of chicken, and 5 fried shrimp, while Platter 2 comes with 3 pieces of fish, 1 piece of chicken, and 8 fried shrimp. Platter 1 sells for 8 dollars and platter 2 sells for 10 dollars. If LJS has access to 1000 pieces of fish, 1200 pieces of chicken, and 2600 fried shrimp, what is the optimal number of platters LJS should make in order to maximize its profit? Note that the constraints relate to (please use these in order) fish, chicken, and shrimp.At Long John Silver’s (LJS), Platter 1 comes with 2 pieces of fish, 3 pieces of chicken, and 5 fried shrimp, while Platter 2 comes with 3 pieces of fish, 1 piece of chicken, and 8 fried shrimp. Platter 1 sells for 8 dollars and platter 2 sells for 10 dollars. If LJS has access to 1000 pieces of fish, 1200 pieces of chicken, and 2600 fried shrimp, what is the optimal number of platters LJS should make in order to maximize its profit? Note that the constraints relate to (please use these in order) fish, chicken, and shrimp. Note that problem 7 had three constraints (excluding the non-negativity constraints), and setting two pairs of those constraints to equality led to two extreme points on the feasible region. What INFEASIBLE point was at the intersection of the other pair of constraints? In the optimal solution to problem 7, the optimum was found at the intersection of two of the constraints that were not non-negativity constraints. Call these “binding” constraints. One of those…