Keeping 3000$ and 5000$ as unit contributions respectively for Model 101 and Model 102 trucks, formulate the Merton’s product mix decision problem using LP. Present the LP problem in the standard form including all the details and units. Using solver, find the optimal product mix of these two trucks? What is the optimum total contribution that Merton can obtain? Tabulate, the optimality range for the decision variable coefficients and comment what will happen if the current unit contribution moves outside the range? Tabulate, the feasibility range for each constraint’s capacity and comment what will happen if the current capacity moves outside the range? Due to increase in Engine component’s 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.
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. 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. 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. Should they produce Model 103 trucks?
How high would the contribution on each model 103 truck have to be before it became worthwhile to produce the new model?