How to answer question (d) & (e)?
Colonial Furniture produces hand-crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and/or armoires over the next week. These products go through two stages of production (assembly and finishing). The following table gives the time required for each item to go through these two stages, the amount of wood requires, and the corresponding unit profits, along with the amount of each resources available next week. Rocking Dining Armoire Available Chair Room Table Assembly (minutes) 100 180 120 3,600 Finishing (minutes) 60 80 80 2,000 Wood (pounds 30 180 120 4,000 Unit Profit $240 $720 $600 A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. For each of the following parts, answer the question as specifically and completely as is possible without re-solving the problem with the Solver. Note: Each part is independent (i.e. any change made in one problem part does not apply to any other parts). a) Suppose the profit per armoire decreases by $50. Will this change the optimal an change production quantities? What can be said about the change in total profit? b) Suppose the profit per table decreases by $60 and the profit per armoire increases by $90. Will this change the optimal production quantities? What can be said about the change in total profit? - | 0. 70 rule c) Suppose a part-time worker in the assembly department calls in sick, so that now four fewer hours are available that day in the assembly department. How much 2 to hims would this affect total profit? Would it change the optimal production quantities? d) Suppose one of the workers in the assembly department is also trained to do finishing. Would it be a good idea to have this worker shift some of his time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change? = (0 0% e) The shadow price and allowable range for the wood constraint are missing from the sensitivity report. What numbers should be there? Explain how you were able to deduce each number.A B C D E F G H Rocking Dining Room Chair Table Armoire Unit Profit $240 $720 $600 Resource Required per Unit Used Available Assembly (minutes) 100 180 120 3,600 3.600 Finishing (minutes) 60 SO SO 2.000 30 3.600 IA IA IA 2.000 Wood (pounds) 180 120 4.000 10 Rocking Dining Room 11 Chair Table Armoire Total Profit 12 Production 0 10 15 $16.200 13 Variable Cells Cell Name Final Reduced Objective Allowable Allowable Value Cost Function Increase Decrease SBS12 Production Chair 0 -230 240 230 1E+30 SC$12 Production Table 10 0 720 180 120 SD$12 Production Armoire 15 0 600 120 120 Constraints Cell Name Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease SES6 Assembly (minutes) Used 3,600 2.00 3,600 400 600 SES7 Finishing (minutes) Used 2,000 4.50 2,000 400 400 SES8 Wood (minutes) Used 3.600 4,000
