OPERATIONS RESEARCH (TERM-2, PGP-1)PRE-MIDTERM ASSIGNMENT Analyze the Merton trucks case given in Lecture-8 and respond to the questions listed below using excel solver. Ensure in the Excel solver formulation that relevant descriptions and units are given for decision variables, objective function and all the constraints. This is to ensure that appropriate description will be automatically generated in the answer report and sensitivity report. Apart from answering the questions below in the assignment, keep printout of your solver outputs (answer and sensitivity report) as is in the assignment hard-copy including the header information. Refer to sample answer report in the last page. Dont edit or make any changes to the report generated by excel-solver. The solver output must be an exact match of the excel file submitted with the assignment. The solver file should be named as RegistrationNumber_Section-ID_Merton.xls. (E.g. 2014103_Sec-D_Merton.xls). The solver file must include formulation, answer report and sensitivity report. A hard-copy assignment report containing response to the questions below in the same order must be submitted by 1-Nov-2014, 1229pm to Mrs. Poornima in the first floor of faculty block. The excel solver file must be submitted by email to myassignments14@gmail.com with email subject as RegistrationNumber Section-ID GIM (e.g. 2014103 Section-D GIM) by 1-Nov-2014, 1229pm. This is an individual assignment. Any indulgence in academic malpractices, including copying in part or full will be punished severely. If you dont adhere to all the instructions, you can expect to be penalized with negative marks or zero.

MERTON TRUCKS COMPANY1. Keeping 3000$ and 5000$ as unit contributions respectively for Model 101 and Model 102 trucks, formulate the Mertons product mix decision problem using LP. Present the LP problem in the standard form including all the details and units.2. Using solver, find the optimal product mix of these two trucks? What is the optimum total contribution that Merton can obtain?3. Tabulate, the optimality range for the decision variable coefficients and comment what will happen if the current unit contribution moves outside the range?4. Tabulate, the feasibility range for each constraints capacity and comment what will happen if the current capacity moves outside the range?5. Due to increase in Engine components material cost, the unit contribution for Model 101 came down to $2000. Do you recommend Merton to continue producing the optimal product mix as found in Question 3? Justify your response with appropriate reasoning.6. Due to repairs in the metal stamping department, the monthly availability of machine-hours came down by 400 hours. Will it affect the optimal contribution? If yes, by how much? If no, why not? Justify your response with appropriate reasoning.7. Convert Two-truck product mix LP (primal, question -1) into canonical form. Formulate the dual for the two trucks decision problem in the standard form including all the details and units.8. Merton is considering the introduction of a new truck, to be called Model 103. Each model 103 truck would give a contribution of $1800. The total engine assembly capacity would be sufficient to produce 5000 model 103s per month, and the total metal stamping would be sufficient to produce 4000 Model 103s. The new truck would be assembled in the Model 101 assembly department, each model 103 truck requiring only half as much time as a Model 101 truck. Keep a printout of the answer and sensitivity report with header for three trucks case. You need not submit this excel file by email for three trucks case. However, keep your three trucks case excel file safely.a. Should they produce Model 103 trucks?b. How high would the contribution on each model 103 truck have to be before it became worthwhile to produce the new model?

Microsoft Excel 15.0 Answer Report

Worksheet: [4. Problem set - 3 -Wyndsor.xlsx]Sheet1

Report Created: 11/Oct/2014 09:21:58

Result: Solver found a solution. All Constraints and optimality conditions are satisfied.

Solver Engine

Engine: Simplex LP

Solution Time: 0 Seconds.

Iterations: 2 Subproblems: 0

Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Max)

CellNameOriginal ValueFinal Value

$B$7Maximise weekly profit (in thousand $)036

Variable Cells

CellNameOriginal ValueFinal ValueInteger

$B$3Product-102Contin

$C$3Product-206Contin

Constraints

CellNameCell ValueFormulaStatusSlack

$E$11Plant-1 capacity in hours2$E$11