Destination: Source 1 2 3 Demand 1 324 3 Unit Cost (5) 2 7 4 3 3 3 638 6 3 8 2 4 425 2 Supply S 2 3 523 a. Draw the network representation of this problem. b Display the problem on a spreadsheet and then use the Excel Solver to obtain an optimal solution.
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- Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.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☆1. Explain the meaning of the expected value of perfect information (EVPI) in this problem. Based on the results of (iii) and (iv), which investment would you choose? 2. Compute the coefficient of variation, the return-to-risk ratio (RTRR) for each investment. Based on (vii) and (viii), what investment would you choose? Compare the results of (vi) and (ix) and explain any differences
- 3. Consider the transportation problem having the following parameter table: Source Demand Source 1 Source 2 650 Source 3 400 1 2 3 Destination 1 Destination 2 500 750 Demand 10 Vj Assume we have obtained an initial BF solution from northwest corner method, it is: X11 = 10, X12 = 2, X22 = 8, X23 = 9, So the initial transportation simplex tableau looks like below. (Boxed values are cost values, X33 = 1, X34 = 10 circled values are basic variable values.) V₁ = Destination 2 750 800 700 10 1 500 650 400 10 10 800 700 10 ܠ ܕܐ 2 3 300 400 500 10 8 400 500 Destination 3 Destination 4 300 450 10 4 450 600 550 10 9 1 600 Supply 12 550 10 V₁ = 17 11 (10 Supply 12 17 11 Ui U₁² 0 = U₂ = Uz = Do the optimality test (by finding out all u₁, v₁, and čij values, fill all these values in the above table) to determine if the current solution is optimal or not.Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimalityA linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 1 $0.50 $0.70 2 $0.45 3 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings Indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The Individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean Aroma Rating Taste Rating 75 85 60 85 450 87 550 74 350 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (In pounds) that will meet the quality standards and provide 1,000 pounds of the blended coffee…
- 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 coefficientsA linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 1 $0.50 2 $0.70 3 $0.45 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean Aroma Rating Taste Rating 75 85 60 85 lb lb lb 450 87 650 74 450 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (in pounds) that will meet the quality standards and provide 1,000 pounds of the blended…Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)
- Problem1 Acme Manufacturing Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next 4 months is shown in the following table along with the expected production costs and the expected Month Demand Production Cost Production Capacity 1 420 $49.00 500 a) Formulate an LP model for this problem. b) Create a spreadsheet model for this problem and solve it using Solver. 2 580 $45.00 520 3 310 $46.00 450 4 540 $47.00 550 capacity for producing these items. Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how…Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). C) again). Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem d) Use the Excel solver to do parts b and c. e) follow: Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use…A "What-If" analysis: A department store sells two popular models of wireless headphones, model A and model B. The sales of these products are not independent of each other. Economists call these "substitutable products" because if the price of one increases, more people will choose to substitute the other product and sales of the other will increase. The electronics manager wants to calculate prices that maximize revenue from these two products. Price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model: NA = 18- 0.52 PA+ 0.32 PB Ng= 33+0.18 PA-0.72 PB A spreadsheet for calculating the total revenue for various values of PA and PB is displayed below. It has been designed with the two prices as input parameters that are easily varied. Price A Price B 19 26 Number sold A -18-0.52 B1+0.32 B2 Number sold B -33+0.18 B1-0.72 B2 Total Revenue -B1 B3+B2 B4 Copy-and-paste, or type, the Excel information given above into cells A1:B5 of an…