Exersise3:(а):Define the following terms: Management Science, Feasible region, Feasible Solution, OptimalSolution, Constraints, Extreme point, Objective function, Deterministic Model, Stochastic modeland Sensitive analysis.(b):Find the Range of Optimality for c, and c2 of the following LPP.Max z = 5x1 + 10x2s.t.,2x1 + 3x, < 25X1 + 2 x, < 35andX1, X2 > 0

Management Science: - Management science is a study of different business domains like economics,…

Answered: Exersise3: (а): Define the following…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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%.
Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality
Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.
Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 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
3) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMe
2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)
. Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components' defective rate to be 11%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 74000 acceptable-quality…
9.5 Capital Healthplans Inc. is evaluating two different methods for providing home health services to its members. Both methods involve contracting out for services, and the health outcomes and revenues are not affected by the method chosen. Therefore, the net cash flows for the decision are all outflows. Here are the projected flows: Year Method A ($) Method B ($) 0 (300,000) (120,000) 1 (66,000) (96,000) 2 (66,000) (96,000) 3 (66,000) (96,000) 4 (66,000) (96,000) 5 (66,000) (96,000) What is each alternative’s IRR? If the opportunity cost of capital for both methods is 9 percent, which method should be chosen? Why?
LPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )
Ian Langella faces a decision how large his gasoline station should be. The annual returns wil l depend on both the size of his station and number of marketing factors related to the oil in dustry and demand for gasoline. Ian develop a careful analysis based on the following table: Size of first station Market condition Market conditon Market conditon Good Fair Poor Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000 Develop a decision table for this decision

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