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…

Understanding Business

12th Edition

ISBN:9781259929434

Author:William Nickels

Publisher:William Nickels

Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment

Section: Chapter Questions

Problem 1CE

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8 Graphically find all optimal solutions to the follow- ing LP: min z = x1 - x2 s.t. X1 + x2 < 6 X1 - x2 2 0 X2 - x, 2 3 X1, X2 2 0
4. (Arbitrage) A supplier is selling hammers in two cities, Pleasantville and Happy Valley. It costs him$5.00 per hammer delivered in each city. Let p1 be the price of hammers in Pleasantville and p2 be theprice of hammers in Happy Valley. The price-response curves in each city are:Pleasantville: d1(p1) = 10,000 - 800p1Happy Valley: d2(p2) = 8,000 - 500p2a.) Assuming the supplier can charge any prices he likes, what prices should he charge forhammers in Pleasantville and Happy Valley to maximize total contribution? What are thecorresponding demands and total contributions?b.) An enterprising arbitrageur discovers a way to transport hammers from Pleasantville toHappy Valley for $0.50 each. He begins buying hammers in Pleasantville and shipping themto Happy Valley to sell. Assuming the supplier does not change his prices from those givenin part a, what will be the optimal price for the arbitrageur to sell hammers in Happy Valley?How many will he sell? What will his total contribution be?…
This home work question is based on a "Product Mix" problem For formulations, you don't need to explain it. Just state the formulation and constraints
solve the LP Models asap
Hh4. What is the total cost of meeting customer requirements each day?
Problem 13-03 Algo (Solving Integer Optimization Problems with Excel Solver) Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 1 10 ft. 2 4 0 3 8 4 5 STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: 2 2 Min s.t. 4 3 0 1 3 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types the open market at the selling price. No inventory is held. Pattern (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five…
Friendly Waste Co. runs three different factories and is required by law to safely dispose of chemicals. Waste from three different factories can be processed to reduce the amount of two different types of pollutants. State law requires that the total reduction in the amount of pollutant A is at least 30 tons and pollutant B is at least 40 tons. Using the information in the following table: Factory Proc Cost Per Ton Reduction Plant A Reduction Plant B 1 15 0.1 0.45 2 10 0.2 0.25 3 20 0.4 0.3 •Algebraically formulate a linear programming model to represent this problem.
1. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.
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 =…
3. Hoosier Gasoline Company, or HoosCo as they are known, produces two blends of gasoline, regular and premium, by mixing three different types of oil, indi- cated by Types 1, 2, and 3. Each type of oil comes in barrels and has its own costs and octane readings, which are given below. Type I Type 2 Type 3 Cost/Barrel $45 $35 $20 Octane Rating Regular gasoline Premium gasoline Regular gasoline 93 91 87 To produce each blend of gasoline, we must combine these oils so as to meet the following requirements. Premium gasoline Maximum Available 10,000 15,000 20,000 At least 25% Type 1 At least 35% Type 2 At most 30% Type 3 At least 30% Type 1 At least 45% Type 2 At most 20% Type 3 There are also sales prices, average octane rating requirements for the gasolines, and minimum requirements in production of each blend. Average Octane Rating Sales Price 89 91 $65 $75 Minimum Demand 15,000 barrels 12,500 barrels How much of each type of gasoline should be produced to satisfy all require- ments and…
Variable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…
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