For the linear program MAX 2A+ 3B S.t. 1A+ 2B = 65A+3B <= 15 A, B > = 0 Find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution.
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For the linear program MAX 2A+ 3B S.t. 1A+ 2B = 65A+3B <= 15 A, B > = 0 Find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution.
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- The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1750 B 500 C 1100 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows: Machine Capacity (Units) 1 1550 2 1450 3 1150 Product Machine A B C 1 $0.80 $1.30 $0.70 2 $1.40 $1.30 $1.50 3 $0.80 $0.80 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of product j on machine i.…Need help only with finding the optimal solutionBJ is the manager of a Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow. BJ estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for $3 per case and sell them for $8 per case. However, any unsold case tomorrow will be sold to nearby Cafeterias at a flat price of $2 per case. BJ now needs to decide how many cases to purchase today to be offered for sale tomorrow. BJ has checked the store's records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow. (a) Develop a decision analysis structured model of this problem using Excel formulas by identifying the decision alternatives, the states of nature, and the payoff table. (b)…
- xa cheese factory is making a new cheese from mixing two products a and b, each made of three different types of milk - sheep, cow and goat milk. the compositions of a and b and prices ( $ /kg) are given as follows, amount (litres) per 1000 kg of a and b sheep cow goat cost ($/kg) a 30 60 40 5 b 80 40 70 8 the recipes for the production of the new cheese require that there must be at least 45 litres cow milk and at least 50 litres of goat milk per 1000 kg of the cheese respectively, but no more than 60 litres of sheep milk per 1000 kg of cheese. the factory needs to produce at least 60 kg of cheese per week. a) explain why a linear programming model would be suitable for this case study. Formulate a Linear Programming (LP) model for the factory that minimises the totalcost of producing the cheese while satisfying all constraints.Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of SpeedBuster models produced. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables. Maximize Profit = 123 L+ 139 S 18 L 11 S≤ 3000 5 L+9 S≤2500 L≥ 0 and S≥ 0 (Availability of component A) (Availability of component B) Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and possible profit, SpeedBuster models. This solution gives the which is $ (Type integers or decimals…Solve the following linear programming problem graphically: Maximize Z=3X+5Y Subject to: 4X+4Y ≤48 C1 1X+2Y ≤20 C2 Y ≥2 C3 X, Y ≥0 Part 2 1) Using the line drawing tool, plot constraint C1 by picking two endpoints for the line. 2) Using the point drawing tool, plot the corner points which define the feasible region. The optimal solution is X= ____ and Y= _______ ( round your responses to whole numbers) Maximum Profit is $ _____ ( round your responses to whole numbers)
- Using Excel Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=Solve Using Excel solver in Linear Optimization Problems. Must present the excel solver output including (answer report sensitivity report and limits report) 1. A calculator company produces two models of calculators at two different factories. Factory A can produce 130 scientific calculators and 25 graphing calculators per day. Factory B can produce 70 scientific and 90 graphing calculators per day. It cost $1200 per day to operate Factory A and $900 per day to operate Factory B. If the company needs to produce 460 scientific calculators and 340 graphing calculators for a big order, find the minimum cost to produce the order.(please help)
- 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.Answer the next TWO (2) questions using the following linear programming problem and the corresponding graphical solution: Max subject to Z=30 x₁ +20 x₂ 2 x₁ + 2x₂ ≤8 8 x₁ +4x2 ≤24 X₂ 2 (constraint I) (constraint II) 13. What is the upper bound of the sensitivity range for the coefficient of x₁ in the objective function? a. 60 b. 10 c. 40 d. 20 14. What is the upper bound of the sensitivity range for the Right-Hand Side (RHS) of constraint I? a. 8 b. 12 c. 4 d. 61. 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.
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