4. Consider the linear program in Problem 3. The value of the optimal solution is 48. Sup-pose that the right-hand side for constraint 1 is increased from 9 to 10.Use the graphical solution procedure to find the new optimal solution.Use the solution to part (a) to determine the shadow price for constraint 1.The sensitivity report for the linear program in Problem 3 provides the following right-hand side range informationa.b.C.AllowableConstraintR.H. SideAllowableIncreaseConstraintDecrease2.0004.0001.000Infinite9.00010.00018.0002.8.0004.000What does the right hand side range information for constraint 1 tell vou about theshadow price for constraint 1?d.The shadow price for constraint 2 is 3. Using this shadow price and the right handside range information in part (C), what conclusion can be drawn about the effect ofchanges to the right-hand side of constraint 2?

Linear Programming :- Linear programming (LP, also called linear optimization) could be a method…

Answered: 4. Consider the linear program in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Refer to the following sensitivity report: Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 5 2 1E+30 $B$3 Product_2 175 0 7 1E+30 1 $B$4 Product_3 0 −1.5 9 1.5 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 If the right-hand side of Resource_C increases to 750, which of the following would be true The objective function value will increase by $1.75 The objective function value will decrease by $1.75 The objective function value will increase by $87.50 The objective function value will decrease by $87.50 None of the answer choices is correct
Refer to the following sensitivity report: Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 5 2 1E+30 $B$3 Product_2 175 0 7 1E+30 1 $B$4 Product_3 0 −1.5 9 1.5 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 If the objective function coefficient for Product_1 were decreased to a value of 3, which of the following would be TRUE? The optimal solution would change. The optimal objective function value would stay the same. Product_1 would enter the solution (the final value of the variable Product_1 would be greater than zero). A. 1 only B. 2 only C. 3 only D. 1, 2 and 3 E. Only 1 and 2
#28Even though independent gasoline stations have been having a difficult time, Susan Solomon hasbeen thinking about starting her own independent gasoline station. Susan’s problem is to decide howlarge her station should be. The annual returns will depend on both the size of her station and a numberof marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susandeveloped the following table: GOOD FAIR POORSIZE OF MARKET MARKET MARKETFIRST STATION ($) ($) ($)Small 50,000 20,000 –10,000Medium 80,000 30,000 –20,000Large 100,000 30,000 –40,000Very large 300,000 25,000 –160,000For example, if Susan constructs a…
Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$6 Activity 1 3 0 30 23 17 $C$6 Activity 2 6 0 40 50 10 $D$6 Activity 3 0 –7 20 7 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $E$2 Resource A 20 7.78 20 10 12.5 $E$3 Resource B 30 6 30 50 10 $E$4 Resource C 18 0 40 1E+30 22 Which parameter is most sensitive to an increase in its value?
Course: Management Information Systems 1 MGMT Mobile Company (MMC) offers mobile services to users on a monthly subscription basis.Special discounts are given to customers for frequently using their pre- or post-paid mobile service.Customers can also sign up online or visit one of ten outlets stationed at various locations around thecountry. Customers can opt to receive their bills either through the post or online but all payments are21stdue by the of each month. An 18.5% mobile tax is applied to the cost of all services. All transactions, customer calls and other data are captured in a database, where specific data can beextracted for decision making. As a new employee of a team in the IS Department of this corporation, your manager wants you to produce some reports for him to review for the next quarter, such as which types of customers should be targeted for special offers and how much money is received for taxes.Reports reaching Executive management revealed that all of the…
Course: Management Information Systems 1 MGMT Mobile Company (MMC) offers mobile services to users on a monthly subscription basis.Special discounts are given to customers for frequently using their pre- or post-paid mobile service.Customers can also sign up online or visit one of ten outlets stationed at various locations around thecountry. Customers can opt to receive their bills either through the post or online but all payments are21stdue by the of each month. An 18.5% mobile tax is applied to the cost of all services. All transactions, customer calls and other data are captured in a database, where specific data can beextracted for decision making. As a new employee of a team in the IS Department of this corporation, your manager wants you to produce some reports for him to review for the next quarter, such as which types of customers should be targeted for special offers and how much money is received for taxes.Reports reaching Executive management revealed that all of the…
A wood products firm uses available time at the end of each week to make goods for stock.Currently, two products on the list of items are produced for stock: a chopping board and a knifeholder. Both items require three operations: cutting, gluing, and finishing. The manager of thefirm has collected the following data on these products.TIME PER UNIT (MINUTES)Item Profit/Unit Cutting Gluing FinishingChopping board $2 1.4 5 12Knife holder $6 0.8 13 3The manager has also determined that, during each week, 56 minutes are available for cutting, 650minutes are available for gluing, and 360 minutes are available for finishing.a. Determine the optimal quantities of the decision variables if the goal is to maximize profit.b. Which resources are not completely used by your solution? How much of each resource isunused?
Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P ≥ 0 non-binding constraint: R+(3/2) P≤900 binding constraints: (1/8) R+(1/4) P≤100 and (1/2) R+(1/3) P≤300 redundant constraint R+(3/2) P≤900 1. What is the range of the coeficient, c1, of the decision variable R that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2 2. What is the range of the coeficient, c2, of the decision variable P that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2
Hamdy A. Taha - Operations Research_ An Introduction-Pearson Education Limited (2017) –Page 236-Question 5-6 City Plant 1 2 3 1 $600 $700 $400 2 $320 $300 $350 3 $500 $480 $450 Three electric power plants with capacities of 25, 40, and 30 million kWh supply electricityto three cities. The maximum demands at the three cities are estimated at 30, 35, and25 million kWh. The price per million kWh at the three cities is given in Table 5.25. During themonth of August, there is a 20% increase in demand at each of the three cities, which can be metby purchasing electricity from another network at a premium rateof $1000 per million kWh. The network is not linked to city 3, however. The utility companywishes to determine the most economical plan for the distribution and purchase ofadditional energy Formulate the problem as a transportation model. Find the initial basic feasible solution to the above transportation problem by using…
Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively.The production requirements per unit are as follows: (SEE ATTACHED) Answer the following questions (a-i) using the output below please be brief. If there are twopossible answers one will suffice. Where necessary a range analysis must be shown. a) What is the optimal solution and what is the value of the objective function. b) Which constraints are binding and which constraint show extra capacity? c) 100 hours of manufacturing time became available .Evaluate the effect? Explain.
#3) In the environment of increased competition, a fitness club executive is considering the purchase of additional equipment. They are choosing between Acme, Standard and High Pro. With new equipment they can attract new clients and increase their overall profits. The profits are dependent on the markets demand for the new equipment and brand name recognition. If they go with the Acme equipment, there profit would be $375,000 in a favorable market or -$125,000 in an unfavorable market. If they go with the Standard equipment, there profit would be $250,000 in a favorable market or -$95,000 in an unfavorable market. If they go with the High Pro equipment, there profit would be $175,000 in a favorable market or -$50,000 in an unfavorable market. a) Create a decision table and a decision tree. b) If the executive is an optimistic decision maker, which alternative will he choose? What is the payoff? c) If the executive is a pessimistic decision maker, which alternative will he choose? What…

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