10. Recall the Innis Investments problem (Chapter 2, Problem 39). LettingS = units purchased in the stock fundM = units purchased in the money market fundleads to the following formulation:Min8S +3Ms.t.50S + 100M < 1,200,000Funds available5S +4M >60,000Annual income3,000Units in money marketS, M > 0The computer solution is shown in Figure 3.16.a. What is the optimal solution, and what is the minimum total risk?b. Specify the objective coefficient ranges.c. How much annual income will be earned by the portfolio?d. What is the rate of return for the portfolio?e. What is the dual value for the funds available constraint?f. What is the marginal rate of return on extra funds added to the portfolio? Optimal Objective Value =62000.00000VariableValueReduced CostS4000.000000.00000M10000.000000.00000ConstraintSlack/SurplusDual Value10.00000-0.0566720.000002.166677000.000000.00000ObjectiveAllowableAllowableVariableCoefficientIncreaseDecrease8.00000Infinite4.25000M3.000003.40000InfiniteRHSAllowableAllowableConstraintValueIncreaseDecrease11200000.00000300000.00000420000.00000260000.0000042000.0000012000.0000033000.000007000.00000Infinite

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter8: Evolutionary Solver: An Alternative Optimization Procedure

Section8.7: Portfolio Optimization

Problem 14P

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J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. Atthe beginning of January, Huggys has a 30% market7.9 Conclusion 401share. During any month, 10% of the people whopurchase Huggys defect to brand X, and a fraction0.2a1y2 of customers who usually buy brand X switchto Huggys, where a is the amount spent on advertisingin millions of dollars. For example, if you spend $4million during a month, 40% of brand X’s customersswitch to Huggys. Your goal is to maximize J&J’saverage market share during the next 12 months,where the average is computed from each month’sending share. Determine an appropriate advertisingpolicy. (Hint: Make sure you enter a nonzero trialvalue for each month’s advertising expense or Solvermight give you an error message.)
INCORRECT FORFormulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. (Let BR = pounds of Brazilian beans purchased to produce Regular, BD = pounds of Brazilian beans purchased to produce DeCaf, CR = pounds of Colombian beans purchased to produce Regular, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max 2.033BR+2.582BD+1.868CR+2.418CD INCORRECT Pounds of Regular BR+CR≤900 INCORRECT Pounds of DeCaf BD+CD≤400 INCORRECT
11. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization LP problem, this means: a. if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 5 b. if the RHS for that constraint is increased by one then the optimal objective function value is increase by 5 c. if the RHS for that constraint is increased by 5 then the optimal objective function value is increase by 1 d. if the coefficient of the objective function is increase by 5 then the RHS for that constraint must be increased by 1 12. Sensitivity Analysis generally assumes a. we are considering a change in two input data values at a time b. are considering a change in only one input data value at a time c. we are considering several change in several input data…
At time 0, we have $10,000. Investments A and B areavailable; their cash flows are shown in Table 39. Assumethat any money not invested in A or B earns no interest.Formulate an LP that will maximize cash on hand at time3. Can you guess the optimal solution to this problem? TAB LE 39Time A B0 $1 $01 $0.2 $12 $1.5 $03 $0 $1.0

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