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
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
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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…
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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…

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