If the optimal solution to theproblem of linear programmingX₁X₂S₁S₂S3SOLX₂011/2-1/202X₁10-1/83/83/2S3001-2Z-C,001/41/40Find the value of the target function in two waysusing the relationship between optimal modeland dual model01

Answered: If the optimal solution to the problem…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose that a sporting contest at Adelaide oval, which has capacity for 50000 spectators, draws an average crowd of 40,000, but after the ticket price is increased from $37 to $45 the average crowd size falls to 28,000. Assuming that the crowd size is a linear function of the ticket price, find the optimal ticket price (rounded to the nearest 10 cents) to maximize revenue from ticket sales. Optimal ticket price = $*X
Valencia Products makes automobile radar detectors and assembles two models. LaserStop and SpeedBuster. Both models use the same electronic components. After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of SpeedBuster models produced. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables Maximize Profit 125 L 138 S 18 L+12 Ss5000 6L+8554500 L20 and 520 (Availability of component A) (Availability of component B) GITTE Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the (Type integers or decimals rounded to two decimal places as…
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1a and 2a please written out
Use a graphing calculator or a computer program for the simplex method to solve this linear programming problem. S1 $2 X4 .625 1 0 .5 .375 0 1 0 0 0 0 X1 0 0 1 X2 X3 0 .375 .75 .25 125 0 -105-80 -75 - 65 S3 = 0 530 0 630 1 280 0 0 The optimal solution X₁ = ‚ X₂ = ₁ ×3 = (Do not round until the final answer. Then round to the nearest integer as needed.) and X4 = produces the maximum value
Graph the constant-cost lines for the objective function C = 4x+ 5 y through (8,8) and also through (12,12). Use a straightedge to identify the corner point where the minimum cost occurs. Confirm your answer by constructing a corner point table. 15+ (0,15) (0,11) 10-1 5- (2,3) T 5 (12,12) (8,8) (15,15) 10 (15,0) Q Q M Which graph below has the correct constant-cost lines? O A. O B. 15 10- O C. 15+ 10-1 5- 5 10 15 5 10 15 Q M Q 37 15 10- 5- O D. 15- 10- 5- 5 10 15 -10 5 '10' 15 Q Q Q 37
Explain important characteristics of situations to which linear programming method can be successfully applied. Assume a suitable example A firm manufactures three products A, B, and Time to manufacture product A is twice that for B and thrice that for C and if the entire labour is engaged in making product A, 1,600 units of this product can be produced. These products are to be produced in the ratio 3:4:5. There is demand for at least 300, 250 and 200 units of products A, B and C and the profit earned per unit is sh. 90, sh. 40 and sh. 30 respectively. Table Raw material Requirement per unit of product (kg) Total availability (kg) A B C P 6 5 2 5,000 Q 4 7 3 6,000 Formulate the problem as a linear programming problem.

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If the optimal solution to the problem of linear programming X₁ X₂ S₁ S₂ S3 SOL X₂ 0 1 1/2 -1/2 0 2 X₁ 1 0 -1/8 3/8 3/2 S3 0 0 1 -2 Z-C, 0 0 1/4 1/4 0 Find the value of the target function in two ways using the relationship between optimal model and dual model 0 1