Operations Management: Processes and Supply Chains (12th Edition) (What's New in Operations Management)
12th Edition
ISBN: 9780134741062
Author: Lee J. Krajewski, Manoj K. Malhotra, Larry P. Ritzman
Publisher: PEARSON
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Chapter D, Problem 10P
A
Summary Introduction
Interpretation: To maximize the profits for the given constraints and objective function.
Concept Introduction: To obtain the objective function is to maximize or minimize the
B
Summary Introduction
Interpretation: In linear programming, find the better optimal solution using graphic method.
Concept Introduction: In linear programming, graphic method are used to solve the problems by the point of intersection (higher and lower points) between the objective function and regional value of the graph.
C
Summary Introduction
Interpretation: To Determine the constraints with slack or surplus.
Concept Introduction: In Linear Programming, some mathematics oriented problem will be solved by slack variable and surplus variable. Slack variables is defined as less than (<) or equal (=) type of constraints to getting the equality constraint. Surplus variables is termed as greater than (>) or equal (=) type of constraints to getting the equality constraint.
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The ABC Firefighting Equipment company has two assembly plants: Plant A in Atlanta and plant B in Buffalo. It has two distribution centers: Center I in Savannah and center II in Pittsburgh. The company can product at most 800 alarm valves per week at platn A and at most 1000 per week at plant B. Center I must have at least 900 alarm valves per week and center II must have at least 600 alarm valves per week. The costs per unit for transportation from the plants to the centers follow.
Plant A to center I $8
Plant A to center II $12
Plant B to center I $16
Plant B to center II $4
Form the constraint inequalities that give the limits for the plants and distribution centers and form the total cost function that is to be minimized.
Solve the mixed constraint problem for the minimum transportation cost.
Determine whether any shipment route is unnecessary.
Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.
Factory/DCs
Shipping Costs ($ per skateboard)
Iowa 4
Maryland 5
Idaho 6
Arkansas 7
Detroit 1
25.00
25.00
35.00
40.00
Los Angeles 2
35.00
45.00
35.00
42.50
Austin 3
40.00
40.00
42.50
32.50
Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff,…
A company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
Chapter D Solutions
Operations Management: Processes and Supply Chains (12th Edition) (What's New in Operations Management)
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- XYZ Corporation operates two plants, each of which has a capacity of 100 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 20 units per day while customer D has a demand of 140 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 24 21 19 18 Plant 2 18 16 19 10 How many units should XYZ ship from each plant to each customer? (Leave no cells blank—be certain to enter "0" wherever required. Round your answer to the nearest whole number.) What is the least XYZ will spend on shipping each day? (Round your answers to 2 decimal places.)arrow_forwardXYZ Corporation operates two plants, each of which has a capacity of 140 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 11 units per day while customer D has a demand of 247 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 12 18 21 10 Plant 2 16 14 18 20 How many units should XYZ ship from each plant to each customer? Customer A Customer B Customer C Customer D Plant 1 Plant 2 What is the least XYZ will spend on shipping each day?arrow_forwardTransportation Problem: A semi-products manufacturer has 3 production facilities (X, Y, Z) and distributes its products to 3 various customers (K, L, M) from these production facilities. The daily production capacity of each production facility and the daily distribution costs are given in the below table. Daily demands of customers are 42, 27, and 33, respectively. Namely, in a day, customer K requires 42 units of products, customer L requires 27 units of products, and customer M requires 33 units of products. (a) Formulate a balanced transportation problem that could be used to determine how to minimize the total cost of meeting the demand of customers. The formulation should be in open form and decision variables should be defined as integer amounts. (b) Use LINGO/OPL/EXCEL to solve your model. Write down the results of the decision variables and the objective function. Explain the value of the decision variables. What do they mean? (c) Use the Northwest Corner method to find a…arrow_forward
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