Consider the following linear programming problem. 2A + 3B Min s.t. 1A + 4B ≤21 2A + 1827 3A +1.58 21 -2A +6820 A, B 20 (a) Find the optimal solution using the graphical solution procedure and the value of the objective function. at (A, B)=( (b) Determine the amount of slack or surplus for each constraint. slack for 1A + 48 s 21 surplus for 2A +18 2 7 slack for 3A + 1.58 s 21 surplus for -24 + 68 20 (c) Suppose the objective function is changed to max 8A + 3B. Find the optimal solution and the value of the objective function. at (A, B) =
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- 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___________Assuming that the company is interested in maximizing the total profit contribution, answer the following: A, What is the linear programming model for this problem? Decision Variables: LP Model: B.Find the optimal solution using the graphical solution procedure. 1.Feasible Region:2. Identify the binding constraint/s:3. Identify the rebundant constraint/s:4.How many gloves of each model should Kelson manufacture?5.What is the total profit contribution Kelson can earn with the given production quantities? C.How many hours of production time will be scheduled in each department? D.What is the slack time in each department? E.Compute the range of optimality for the objective function coefficientsAsap ppz Three electricity generating firms are competing in the market with the inverse demand given by P[Q) = 21-Q. All firms have constant marginal costs. Firm 1's marginal cost is MC=5; it has a capacity constraint of K1= 5 units. Firm 2's marginal cost is MC 8; it has a capacity constraint of K2 = 3 units. Firm 3's marginal cost is MC = 10; it has a capacity constraint of K3= 3 units.A. The three firms compete in the style of Cournot. Please compute the Nash equilibrium quantities. Also compute the price in the Nash equilibrium.B. Which of these firms would have produced a larger quantity if it had a larger capacity? Please explain.
- 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 =…Q2 Q2: For the following LP model, find values of the first iteration tableau variables using simplex method, in case that A is selected as .an entering variable Q2 Consider the following linear programming problem: Max 3A + 3B s.t. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°C
- An XYZ company has a W, H, O plant with a monthly production capacity of 60 tons, 50 tons, and 42 tons, respectively; and has 3 sales warehouses in cities A, B, C, D Where each warehouse has a monthly requirement of 30 tons, 34 tons, 44 tons and 25 tons. With shipping cost W to ABCD = IDR 12,000,-, IDR. 8.000,-, Rp. 12.000,-, Rp. 14,000,-; H to A B C D = Rp. 8.000,-, Rp. 18.000,-, Rp. 10,000,-, Rp. 6.000,-; and O to ABCD = Rp. 16.000,-, Rp. 16.000,-, Rp. 2,000, Rp. 10,000,-. Please calculate using Vogel's Approximation Method or VAM Question a. What is the best transportation model in your opinion to solve the above problems? b. What is the minimum transportation cost to solve the shipping transportation problem! c. Based on these calculations, give suggestions regarding the transportation model and the amount of costs incurred by the company!Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimalityPlease
- Please answer it immediately sir Linear Programming The Booboo sawmill in Batangas produces pine and oak boards for manufacturing firms. Each month the sawmill must deliver atleast 5 tons of wood to the manufacturer . It takes the sawmill 3 days to produce a ton of pine and a 2 days to produce a ton of oak and the sawmill can allocate 18 days out of a month for this contract. The sawmill can get enough pine to make atleast 4 tons of wood and enough oak to make atmost 7 tons of wood. Determine the number of tons of pine and oak in order to minimize cost, given that pine has a cost of $3 and oak $6 to produceA manufacturer produces two types of calculator; each requiring material and labour as shown below: Input Scientific Calculator Graphic Calculator Availability Labour (hrs) 4 5 200 Inspection time 2 1 80 Material (cm2) 10 12 600 PROFIT $200 $300 Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profitFor the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.