Please use graphic tools and algebric method to answer the question On LP Sensitivity AnalysisFor each of the following two LP models, respond to the following questions using graphic toolsand algebraic methods only:a) Identify the constraints that are binding and the ones that are not binding.b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibilityregion)c) Find the range of optimality of both of the objective function coefficientsd) Find the shadow prices of each of the constraintse) Compute the amount by which the objective function changes, if the right-hand side ofone of the constraints increases by 8%.Model 1:Maximize f = 4x + 7y subject to the following constraints:x+2y≤75x+3ys12y≤3x and y are non-negativeModel 2Maximize f = 7x + 5y subject to the following constraints:3x + 4y < 242x + 1y ≤ 10x ≥ 1y ≤ 5x and y are non-negative

We shall answer first three subparts of the first question only. For others kindly post again by…

Answered: For each of the following two LP…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 40E

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What is the shadow price for the resource C constraint?
On LP Sensitivity Analysis For each of the following two LP models, respond to the following questions using graphic tools and algebraic methods only: a) Identify the constraints that are binding and the ones that are not binding. b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility region) c) Find the range of optimality of both of the objective function coefficients d) Find the shadow prices of each of the constraints e) Compute the amount by which the objective function changes, if the right-hand side of one of the constraints increases by 8%. Model 1: Maximize f = 4x + 7y subject to the following constraints: x+2y≤7 5x+3ys12 y≤3 x and y are non-negative Model 2 Maximize f = 7x + 5y subject to the following constraints: 3x + 4y < 24 2x + 1y ≤ 10 x ≥ 1 y ≤ 5 x and y are non-negative
to part a, write the linear constraints necessary to enforce this restriction. 2) We have just solved a product-mix problem with 4 types of products (W, X, Y, Z), where the total profit (in $ US) is maximized and Excel Solver generates the sensitivity report given in the Table below. Please pick the best answer for the following questions regarding sensitivity analysis and give explanation for each answer. Variable Cells Objective Coefficient 450 Final Reduced Allowable Allowable Name Value 23.36 Cost Increase 300 Decrease 66.67 42.86 1E+30 Y 17.55 0. 1150 350 ??? 27.27 27.27 800 300 W ?2? -95.45 95.45 IE+30 Constraints Constraint Final Shadow Allowable Allowable Decrease Increase 1E-30 Name Value Price R.H. Side 254.55 5545.45 730 29200 33590 91 5800 730 29200 60500 Resouree 1 Resource 2 71.82 280 193 2800 8566.67 Resource 3 0.18 1E-30 26909.09 Resource 4 0.
A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and K plant I needs at least 32 engines. The company can send at most 140 engines to these assembly plants. It costs $30 per engine to ship to plant I and $50 per engine to ship to plant II. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant II gives similar $15 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? olve this # 3 20 E D View an example Get more help. C How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant I is The number of engines to send to plant II is $ 4 200 R F V % 5 2 T G A B Y H & 7 N ♫ U C J n * 00 A I M ( 9 K Clear…
fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method. A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it must have a daily trucking capacity of at least 84,000 cubic feet. Two types of trucks are appropriate for the specialized operation. Their characteristics and costs are summarized in the table below. Note that truck two requires three drivers for long haul trips. There are 41 potential drivers available, and there are facilities for at most 40 trucks. The businessman's objective is to minimize the total cost outlay for trucks. Capacity Drivers Truck Cost (cu. ft.) Needed Small $18,000 2,400 1 Large $45,000 6,000 3 Solve the problem graphically and note that there are alternative optimal solutions. Which optimal solution uses only one…
Explain how the various changes to LP affect the optimal solution. a) Changes to the objective function coefficient b) Changes to the RHS of a constraint
5. What does the Lagrange multiplier in a problem of constrained optimisation measure? Assume a problem of maximising an increasing and concave objective function on a strictly convex feasible set defined by a single strictly increasing and convex constraint. What value would you expect the Lagrange multiplier to take in the solution to such a problem (positive, negative, or zero)? Explain your answer as carefully as you can.
Solve the following LP model. a. Develop a spreadsheet model and find the optimal solution using Excel Solver.b. What is the optimal solution? What is the optimal objective function value? Maximize P = 2x1 + 9x2Subject to 2x1 + 3x2 <= 30 2x1 + x2 <= 16 x1 - x2 <= 0 x1 ≥ 0, x2 ≥ 0

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