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Problem 1
Solve the LOGO Production problem (the base version with only two products — see attached Download Excel file) with Excel Solver and produce the Sensitivity Report. Using the sensitivity report without resolving the problem, predict whether the optimal solution changes if:
In each case where the optimal solution does not change, also predict the new optimal profit without resolving the problem. Show your workings.
Problem 2
Refer to the Sensitivity Report of the LOGO Production problem. Without resolving the problem, predict the optimal profit (or indicate that we cannot predict without resolving) if:
Show your workings.
Problem 3
Refer to the Worker Scheduling problem in Section 4.3 of the textbook. Implement the model in Excel following the textbook.
Then, try to add the following requirement to the model: Out of all workers, we want at least 20% starting their shifts in the weekend (Sat or Sun). For example, if we schedule 5 workers in each 5-day shift, we have 10 out of 35 workers (28.5%) starting their shifts in the weekend, which satisfies the requirement. Can such a requirement be formulated as a linear constraint?
Add this to the spreadsheet model and solve for the optimal solution. How much does adding this constraint change the optimal objective?
Problem 4
A bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds, 10%; home loans, 16%; auto loans, 13%; and personal loans, 20%. To ensure that the bank’s portfolio is not too risky, the bank’s invest- ment manager has placed the following three restric- tions on the bank’s portfolio:
Problem 5
Young MBA Erica Cudahy can invest up to $20,000 in stocks and loans. Each dollar invested in stocks yields $0.08 profit, and each dollar invested in a loan yields $0.13 profit. At least 40% of all money invested must be in stocks, and at least $7000 must be in loans. Determine how Erica can maximize the profit earned on her investments.
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