Use the following Excel output to answer the following questions. a) Write only the objective function. b) What is the optimal solution? Give the values for all variables.c) Write the objective function value.d) In the original problem, if the right hand side of constraint #2 were increase to 321, how would it change objective function value? Sensitivity ReportVariable CellsCellName$B$3 Number of units ESCS3 Number of units S$D$3 Number of units DConstraintsName$E$6 Constraint 1$E$7 Constraint 2$E$8 Constraint 3Final Reduced Objective Allowable AllowableValue Cost Coefficient IncreaseDecrease801200FinalValue20032020800ShadowPrice313206395135Constraint Allowable AllowableR.H. SideIncreaseDecrease200320240015.581E+3080801E+3040120320 Number of unitsMax ProfitConstraintsConstraint 1Constraint 2Constraint 3EAnswer ReportObjective Cell (Max)CellName$E$4 Max Profit8063ConstraintsCellName$E$6 Constraint 1$E$7 Constraint 2$E$8 Constraint 3118Variable CellsCellName$B$3 Number of units E$C$3 Number of units S$D$3 Number of units DS120951212D0135Cell Value1000+14LHS16440Original Value Final Value016440200<=320 <=2080 <=Original Value Final ValueSignInteger80 Contin120 Contin0 ContinFormula200 $E$6<=$G$6 Binding320 $E$7<=$G$7 Binding2080 $E$8<-$G$8 Not BindingRHSStatus Slack02003202400320

Sensitivity report is a tabular representation of results derived from sensitivity analysis. Report…

Use the following Excel output to answer the following questions. a) Write only the objective function. b) What is the optimal solution? Give the values for all variables. c) Write the objective function value. d) In the original problem, if the right hand side of constraint #2 were increase to 321, how would it change objective function value?

Use the following Excel output to answer the following questions. a) Write only the objective function. b) What is the optimal solution? Give the values for all variables. c) Write the objective function value. d) In the original problem, if the right hand side of constraint #2 were increase to 321, how would it change objective function value?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 40P

See similar textbooks

Similar questions

This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
Globex Investment Capital Corporation owns six companies that have the following estimatedreturns (in millions of dollars) if sold in one of the next 3 years:Year Sold(Estimated return, $1,000,000s)Company 1 2 31 14 18 232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28To operating funds, the company must sell at least $24 million worth of assets in year 1, $28million in year 2, and $32 million in year 3. Globex wants to develop a plan for selling thesecompanies during the next 3 years to maximize return.(a) Formulate an integer programming model for this problem.
1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1
Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????
Consider the following linear program: MAX 3x1 + 4x2 ($ Profit) s.t. x1 + 3x2 £ 12 2x1 + x 2 £ 8 x1 £ 3 x1, x2 ³ 0 The Management Scientist provided the following solution output:OPTIMAL SOLUTIONObjective Function Value = 20.000 Variable Value Reduced Cost X1 2.400 0.000 X2 3.200 0.000 Constraint Slack/Surplus Dual Price 1 0.000 1.000 2 0.000 1.000 3 0.600 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 1.333 3.000 8.000 X2 1.500 4.000 9.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 9.000 12.000 24.000 2 4.000 8.000 9.000 3 2.400 3.000 No Upper Limit a. What is the optimal solution including the optimal value of the objective function? b. Suppose the profit on x1 is…
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 10 grams of creatine, 42 grams of L-glutamine, and 96 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtends = ervings of gainz =
ABC Woodcarving manufactures two types of wooden toys: soldiers and trains. A soldier sells for $29 and uses$10 worth of raw materials. Each soldier that is manufactured increases ABC’s variable labor and overhead costsby $12. A train sells for $22 and uses $7 worth of raw materials. Each train built increases ABC’s variable laborand overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor:carpentry and finishing. A soldier requires 4 hours of finishing labor and 3 hour of carpentry labor. A train requires2 hour of finishing and 1 hour of carpentry labor. Each month, ABC can obtain all the needed raw material but only4,200 finishing hours and 2,000 carpentry hours. Demand for trains is unlimited, but at most 220 trains are boughteach month. ABC wants to maximize monthly profit (revenues – costs). Formulate an LP model that can be used tomaximize ABC’s monthly profit. (a) Step 1: Define the decision variables precisely and completely…