(a) Solve the problem by inspection (do not use the Gauss- Jordan row operations), and justify the answer in terms of the basic solutions of the simplex method. (b) Repeat (a) assuming that the objective function calls for minimizing z = X₁
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OPERATIONS MANAGEMENT. (ALREADY ANSWERED IN BARTLEBY. DO NOT COPY THE ANSWER HERE.)
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- Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S1Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40 x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 1? Choices: A. Entering Variable: y and Leaving Variable: S1 B. Entering Variable: x and Leaving Variable: S1 C. Entering Variable: x and Leaving Variable: S2 D. Entering Variable: y and Leaving Variable: S2
- 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.Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤100 (C1) 1X1+2X2≤100 (C2) X1,X2≥0 Part 2 The optimum solution is: Part 3 X1= ______ (round your response to two decimal places).
- Consider the following linear programming problem: Maximize 6x+5y (OBJ) Subject to x+y≤6 (1) 2x+y≤8 (2) y≤5 (3) x,y≥0 What is the optimal solution to this problem? What is the optimal value of the objective function? Solve this model by using graphical analysis based on the Corner Point Solution Method. Answer questions below. 2.1. Clearly plot and label the constraints. Show your calculations for drawing constrain line. The solution without calculation will not be accepted. 2.2. Develop and shade the feasible region. Use graph paper. 2.3. Compute all the corner points or extreme points and their coordinates (i.e. the values of x and y). The solution without calculation will not be accepted. 2.4. Determine the optimal solution (i.e. the values of x and y) using corner points method. Why your solution is optimal? 2.5 Compute the value of the objective function at the optimal…Min z = 4x1 + 2x2 s.t. 3x1 + x2 ≥ 27 -x1 - x2 ≤ 21 x1 + 2x2 ≥ 30 x1 and x2 are unrestricted . Solve using simplex methodSet up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .
- Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 7x + 14y + 4z subject to the following. 3x + 5y + 4z ≤ 30 3x + 2y ≤ 4 x + 2y ≤ 8 (x,y,z)= f=LINGO SOFTWARE Consider a production-mix problem where we are concerned with what mix of four products we should produce during the upcoming week. For each product, each unit produced requires a known amount of production time on each of the three machines. Each machine has a certain number of hours of production time available per week. Each product provides a certain profit per unit produced. Figure 3S1.2 shows three types of data: machine-related data, product-related data, and data related to combinations of a machine and product. The objective is to determine how much to produce for each product so that total profit is maximized while not exceeding the limited production capacity of each machine. Requirement: Solve this problem in LINGO software.Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.