For the following transportation problem find the optimal Solution by using * :Multipliers method 1 2 3 4 supply 10 8 12 14 100 350 100 150 7 13 11 50 300 225 25 4 300 9. 10 5 300 demand 350 225 100 125 150 1, 2. 3.
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- Define the term constraint.Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex methodA retail store in Des Moines, Iowa, receives shipments of a particular product from KansasCity and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolisa. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost$0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model…
- 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.solve for y in part bExplain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.
- City government has collected the following data on annual sales tax collections and new car registrations: Annual Sales Tax Collections (in millions) 1.0 1.4 1.9 2.0 1.8 2.1 2.3 2.5 New Car Registrations (in millions) 10 12 15 16 14 17 20 22 Determine the following: Plot these data and decide if a linear model is reasonable. Using the results of part a., find the estimated sales tax collections if new car registrations total 25,000,000.KOOKABOORA CONTAINER CORPORATION (From Business Organization and Management – Dr. Roberto Medina) When the Clark Special Economic Zone in Pampanga opened its gates for investors in light and medium industries, the Kookaboora Container Corporation (KCC) was among the first ten companies to locate in the zones’s premises. KCC manufactures containers of various shapes and sizes which are used by manufacturers of industrial chemicals, food products, cooking oil, motor oil and others. The production department of KCC is headed by Engr. Nicolas, a licensed mechanical engineer. He is a tickler for discipline. When even small mistakes happen in his department, he personally calls the offending employee and metes appropriate penalty. As a result, his department was judged best in efficiency. Very minimal wastage in materials and time were recorded by the department. Under the direct supervision of Engr. Nicolas are 10 supervisors who are graduates of engineering courses and…eBook Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Room Type 1 Type II Rental Class Super Saver $37 $18 Explain. Deluxe $40 $33 Variable SuperSaver rentals allocated to room type I SuperSaver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Is the demand by any rental class not satisfied? Business Type 1 rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 125 rentals in the Super Saver…
- given the transportation problem, assume that the demands at the 4 destinations are 5, 5, 7, and 8 units, respectively, and the supplies at the 4 sources are 7, 3, 7 and 8 units, respectively.C₁₁=7ㅤ C₁₂=9ㅤ C₁₃ = 1ㅤ C₁₄ = 10 C₂₁= 22ㅤ C₂₂ = 25ㅤ C₂₃ = 16ㅤ C₂₄ = 26 С₃₁ = 28ㅤ C₃₂ = 32ㅤ C₃₃ = 24ㅤ Сз₄ = 32 C₄₁ = 12ㅤ C₄₂ = 14ㅤ C₄з = 6ㅤ C₄₄ = 16where m=4, n=4what is the optimal solution using vogel's approximation method, least-cost method, and northwest-corner rule?KOOKABOORA CONTAINER CORPORATION (From Business Organization and Management – Dr. Roberto Medina) When the Clark Special Economic Zone in Pampanga opened its gates for investors in light and medium industries, the Kookaboora Container Corporation (KCC) was among the first ten companies to locate in the zones’s premises. KCC manufactures containers of various shapes and sizes which are used by manufacturers of industrial chemicals, food products, cooking oil, motor oil and others. The production department of KCC is headed by Engr. Nicolas, a licensed mechanical engineer. He is a tickler for discipline. When even small mistakes happen in his department, he personally calls the offending employee and metes appropriate penalty. As a result, his department was judged best in efficiency. Very minimal wastage in materials and time were recorded by the department. Under the direct supervision of Engr. Nicolas are 10 supervisors who are graduates of engineering courses and…A firm produces a product at two factories and sells the product at two retail stores. The firm has two warehouses to which all products are shipped for distribution to retail stores. Units are always shipped from the factories to the warehouses and then distributed to the retail stores from the warehouses. The firm wants to determine the shipping pattern from factories to warehouses to retail stores that will minimize cost. The various unit shipping-costs are: Source Data. From To: W1 To: W2 F1 8. F2 3 6. Source Data. From To: R1 To: R2 W1 5 8. W2 3 6. Note: The production capacities at the factories and the demand at the retail stores are: Products can also be shipped from factory 2 (F2) to factory 1 (F1). The cost for that is 3 per unit. Factories Retail Stores F1: 100 R1: 140 F2: 200 R2: 160