5.20. Reconsider Problem 5.13 . Now suppose that all of the parameters are uncertain, with ranges of uncertainty as given in the table below. Use the procedure for robust optimization with independent parameters to find the solution that maximizes profit when the solution also is guaranteed to be feasible. Resource Usage per Unit of Each Activity Resource 1 2 Amount of Resource Available 1 0.81.2 0 3.64.4 2 0.91.1 2.53.5 13.516.5 3 1.62.4 0.71.3 89.510.5 Unit Profit $290$310 $130$220 5.12. Consider a resource-allocation problem having the following data: Resource Usage per Unit of Each Activity Resource 1 2 Amount of Resource Available 1 1 3 8 2 1 1 4 Unit profit $1 $2 The objective is to determine the number of units of each activity to undertake so as to maximize the total profit. AS . Use the graphical method to solve this model. . Use graphical analysis to determine the shadow price for each of these resources by solving again Page 195 after increasing the amount of the resource available by one. . Use the spreadsheet model and Solver instead to do parts a and b. . For each resource in turn, use a parameter analysis report to systematically generate the optimal solution and the total profit when the only change is that the amount of that resource available increases in increments of 1 from 4 less than the original value up to 6 more than the original value. Use these results to estimate the allowable range for the amount available for each resource. . Use Solver's sensitivity report to obtain the shadow prices. Also use this report to find the range for the amount of each resource available over which the corresponding shadow price remains valid. . Describe why these shadow prices are useful when management has the exibility to change the amounts of the resources being made available. 5.13. Follow the instructions of Problem 5.12 for a resourceallocation problem that again has the objective of maximizing total profit and that has the following data: Resource Usage per Unit of Each Activity Resource 1 2 Amount of Resource Available 1 1 0 4 2 1 3 15 3 2 1 10 Unit profit $3 $2