dmod1

please answer all parts of the question

spreadsheet template:

During the next production period, The Diego Garcia Furniture Company is considering producing dining room chairs, dining room tables and/or bookcases. Each item must go through the two stages of production (assembly and finishing), and requires a certain amount of wood (fine cherry wood). They have formulated a linear program to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. Variahle Cells For each of the following parts, answer the question as specifically and completely as is possible using just the sensitivity report, without re-solving the problem with the Solver. All problems are independent (i.e., any change made in one problem part does not apply for the other problem parts). justify your answers by utilizing the results in the sensitivity report. a. Suppose the profit per bookcase decreases by $25. Will this change the optimal production quantities? What can be said about the change in total profit? b. Suppose the profit per table decreases by $10 and the profit per bookcase increases by $40. Will this change the optimal production quantities? What can be said about the change in total profit? c. Suppose a part-time worker in the assembly department calls in sick, so that now four fewer hours are available in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? d. Suppose one of the workers in the assembly department is also trained to do finishing. Would it be a good idea to have this worker shift some of her time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change? e. The allowable decrease for the chairs variable cell and the allowable decrease for the wood constraint were both accidentally deleted from the sensitivity report. Based on the nature of the solution, you should be able to infer what numbers were there. For each, indicate what number should be there and, in a sentence or two, explain the intuition as to why you know that particular number should be there. Constraints \begin{tabular}{clcccccc} \hline & & Name & Final & Shadow & Constraint & Allowable & Allowable \\ Cell & \multicolumn{1}{c}{ Nalue } & Price & R.H. Side & Increase & Decrease \\ \hline$E$5 & Assembly (minutes) Total Used & 3600 & 4 & 3600 & 200 & 600 \\ \hline$E$6 & Finishing (minutes) Total Used & 2000 & 5 & 2000 & 400 & 400 \\ \hline$E$7 & Wood (pounds) Total Used & 3600 & 0 & 3800 & 1E+30 \\ \hline \end{tabular} a. Suppose the profit per bookcase decreases by $25. Will this change the optimal production quantities? What can be said about the change in total profit? 22 b. Suppose the profit per table decreases by $10 and the profit per bookcase increases by $40. Will this change the optimal production 24 quantities? What can be said about the change in total profit? c. Suppose a part-time worker in the assembly department calls in sick, so that now four less hours are available in the assembly department. How much 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 her 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? e. The allowable decrease for the chairs variable cell and the allowable decrease for the wood constraint were both accidentally deleted from the sensitivity report. Based on the nature of the solution, you should be able to infer what numbers were there. For each