I. Consider the following lincar program:Max 3A + 28LA+ I8 S 103A + 18 24LA+ 28 16A. B0Use the graphical solution procedure to find the optimal solution.b. Assume that the objective function coefficiet for A changes from 3 to 5. Does theoptimal solution change? Use the graphical solution procedure to find the new optimalsolution.C. Assume that the objective function coefficient for A remains 3, but the objective funetion coefficient for B changes from 2 to 4. Dies the optimal solution change? Use thegraphical solution procedure to find the new optimal solutiond. The sensitivity report for the lincar program in part (a provides the following objec-tive coefficient range information:ObjectiveCoefficientAllowableIncreaseAllowableDecreaseVariableLO0010003.0003.0002000Use this objective coefficient range informution to answer parts (b) and(C 2. Consider the linear program in Problem 1. The value of the optimal solution is 27.Suppose that the right-hand side for constraint 1 is increased from 10 to 11.a Use the graphical solution procedure to find the new optimal solution.b. Use the solution to part (a) to determine the shadow price for constraintI.e. The sensitivity report for the linear program in Problem I provides the following right-hand-side range information:ConstraintR.H. SideAllowableIncreaseAllowableDecreaseConstraint10.00024.00016.0001 2006.000Infinite2.0006.0003.000What does the right-hand-side range information for constraint 1 tell you about theshadow price for constraint 1?d. The shadow price for constraint 2 is 0.5. Using this shadow proe and the night-hand-side range information in part (c), what conclusion can you draw about the effect ofchanges to the right-hand side of constraint 2

Objective Functions and Constraints: Based on the given details, we found the…

Answered: 1. Consider the following lincar…

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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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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
1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________
Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0
Problem 7-41 Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. a. Formulate linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize tota profit contribution. If required, round your answers to two decimal places. L Let R = P =…
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.)
Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…
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Please show how to solve b
Problem 7-19 eBook Given the linear program Max 3A +48 s.t. Y -1A+ 1A + 2A + s.t. 28 ≤ 8 2B ≤ 12 18 ≤ 16 Α, Β 2 0 a. Write the problem in standard form. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Al+ A+ A+C A+ B+ B B+ B B b. Select the correct graph that shows the optimal solution for the problem. S1 S1 + + S₂ + S2 + S3 53 A, B, S1, S2, S3 A Q☆
(d) A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 is $50. How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (iv) (v) Identify the entering, departıng and pivot variables. Use the simplex method to determine the optimal tableau. Ensure that you explain each step in the computation. Identify the basic and non-basic variables. (vii) Identify the optimal solution. (vi)

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