Practical Management Science
5th Edition
ISBN: 9781305250901
Author: Wayne L. Winston, S. Christian Albright
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 53P
a)
Summary Introduction
To determine: The way to minimize the shipping costs.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to bean unfeasible solution.
b)
Summary Introduction
To determine: The common reduction before there is an increase in total cost.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints then it is said to be an unfeasible solution.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Companies A, B, and C supply components to three plants (F, G,
and H) via two crossdocking facilities (D and E). It costs $4 to ship
from D regardless of final destination and $3 to ship to E
regardless of supplier. Shipping to D from A, B, and C costs $3, $4,
and $5, respectively, and shipping from E to F, G, and H costs $10,
$9, and $8, respectively. Suppliers A, B, and C can provide 200,
300 and 500 units respectively and plants F, G, and H need 350,
450, and 200 units respectively. Crossdock facilities D and E can
handle 600 and 700 units, respectively. Logistics Manager, Aretha
Franklin, had previously used "Chain of Fools" as her supply chain
consulting company, but now turns to you for some solid advice.
Set up the solution in Excel and solve with Solver. What are total
costs?
Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice.
What is the objective function?
Group of answer choices
Max Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH
Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH
Min Z = $3AD + $3BE + $5CD + $3CE…
A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1
has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows:
W 1
W 2
W 3
$7.50
$6.75
$6.25
$7.00
$6.50
$8.00
Customer A
Customer B
Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1.
This exercise contains only parts b, c, d, e, and f.
b) The objective function for the LP model =
Minimize Z =
$7.50
+ $6.25
+ $6.50
(shipping cost to customer A)
V +
$6.75
+ $7.00
+ $8.00
(shipping cost to customer B)
c) Subject to:
Customer A's demand
Customer B's demand…
Chapter 5 Solutions
Practical Management Science
Ch. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.3 - Prob. 10P
Ch. 5.3 - Prob. 11PCh. 5.3 - Prob. 12PCh. 5.3 - Prob. 13PCh. 5.3 - Prob. 14PCh. 5.3 - Prob. 15PCh. 5.3 - Prob. 16PCh. 5.3 - Prob. 17PCh. 5.3 - Prob. 18PCh. 5.4 - Prob. 19PCh. 5.4 - Prob. 20PCh. 5.4 - Prob. 21PCh. 5.4 - Prob. 22PCh. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Prob. 25PCh. 5.4 - Prob. 26PCh. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Prob. 29PCh. 5.5 - Prob. 30PCh. 5.5 - Prob. 31PCh. 5.5 - Prob. 32PCh. 5.5 - Prob. 33PCh. 5.5 - Prob. 34PCh. 5.5 - Prob. 35PCh. 5.5 - Prob. 36PCh. 5.5 - Prob. 37PCh. 5.5 - Prob. 38PCh. 5 - Prob. 42PCh. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - Prob. 76PCh. 5 - Prob. 77PCh. 5 - Prob. 80PCh. 5 - Prob. 81PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - Prob. 85PCh. 5 - Prob. 86PCh. 5 - Prob. 87PCh. 5 - Prob. 2C
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?arrow_forwardMount Isa Mines is one of the world’s great metal mines. Its main operations are at Mount Isa, in Queensland, Australia, where it mines adjacent deposits of copper and silver-lead-zinc ores. Production levels change with world demand and prices, but in a typical year, 7 million tonnes of ore are mined to give 150,000 tonnes of copper and lead (containing silver) and 200,000 tonnes of zinc. Mount Isa has serious transport problems. It produces huge quantities of ore in a remote area of Australia, while the main demand for finished metals is in the industrialized areas of the world, particularly Europe. The problem is to process the ores and move them to final markets as cheaply as possible. You can see the scope of the problem from an outline of the journey for copper, this starts with underground explosions to break up the ore body. The broken ore is collected by front-end loaders and put onto ore trains that carry it to underground crushers. The crushed ore is then hoisted to the…arrow_forwardMount Isa Mines is one of the world’s great metal mines. Its main operations are at Mount Isa, in Queensland, Australia, where it mines adjacent deposits of copper and silver-lead-zinc ores. Production levels change with world demand and prices, but in a typical year 7 million tonnes of ore are mined to give 150,000 tonnes of copper and lead (containing silver) and 200,000 tonnes of zinc. Mount Isa has serious transport problems. It produces huge quantities of ore in a remote area of Australia, while the main demand for finished metals is in the industrialized areas of the world, particularly Europe. The problem is to process the ores and move them to final markets as cheaply as possible. You can see the scope of the problem from an outline of the journey for copper, this starts with underground explosions to break up the ore body. The broken ore is collected by front-end loaders and put onto ore trains that carry it to underground crushers. The crushed ore is then hoisted to the…arrow_forward
- Mount Isa Mines is one of the world’s great metal mines. Its main operations are at Mount Isa, in Queensland, Australia, where it mines adjacent deposits of copper and silver– lead–zinc ores. Production levels change with world demand and prices, but in a typical year 7 million tonnes of ore are mined to give 150,000 tonnes of copper and lead (containing silver) and 200,000 tonnes of zinc. Mount Isa has serious transport problems. It produces huge quantities of ore in a remote area of Australia, while the main demand for finished metals is in the industrialised areas of the world, particularly Europe. The problem is to process the ores and move them to final markets as cheaply as possible. You can see the scope of the problem from an outline of the journey for copper. This starts with underground explosions to break up the ore body. The broken ore is collected by front- end loaders and put onto ore trains that carry it to underground crushers. The crushed ore is then hoisted to the…arrow_forwardIs transportation modeling a type of linear programming? Justify your answerarrow_forwardThe Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)arrow_forward
- Joburg Logistics (JL), a distributor of various products in Polokwane receives their products from suppliers in Durban, Cape Town, and Johannesburg. The company's management is concerned with the supply cost of a certain product that is supplied by a manufacturer in Durban. Currently JL has a contract with Transnet Freight Rail (TFR) for the transport of the orders from Durban. The following are the rail rate and transit time: Transit time (rail) Rail rate 5 days R2.75/unit The impact on the transport and inventory carrying cost because of this arrangement is a concern of the logistics director, Mrs Micky. As a result, Mrs Micky has requested the logistics manager to evaluate the option to use a 3PL service provider for the shipment from Durban to Johannesburg. The logistics manager has identified a certain 3PL company that has the capacity to perform this contract. However, in order to provide a transport rate, the 3PL company required the size and frequency of orders. JL currently…arrow_forwardTMA manufactures 37-in. high definition LCD televisions in two separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of televisions to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the two TMA plants to the two Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $6 $3 Location II $7 $8 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x, y) = 2000,4000…arrow_forwardFormulate but do not solve the problem.The management of Hartman Rent-A-Car has allocated $2.25 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $18,000 each, intermediate-size cars cost $27,000 each, and full-size cars cost $36,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.) = 2,250,000 = x = 100arrow_forward
- NTS is a Swiss intermodal operator located in Lausanne. When customers need to transport goods between origin and destination, NTS supplies them with one or more empty containers in which the goods can be loaded.Upon arrival at the destination, the goods are unloaded, and the empty containers must be transported to the pickup point for new customers. Therefore, NTS management needs to reallocate empty containers periodically (every week). The company's focus is on the transportation activity of empty containers, which is very expensive (almost 35% of the total operational costs). In May 2023, several empty containers, totaling 20 containers, need to be reallocated among terminals in Amsterdam, Berlin, Munich, Paris, Milan, Barcelona, and Madrid. The available or requested number of empty containers at various terminals is reported, along with the transportation costs (in euros per container) as seen in Figure 1. Determine how to solve the problem with the goal of minimizing…arrow_forwardNTS is a Swiss intermodal operator located in Lausanne. When customers need to transport goods between origin and destination, NTS supplies them with one or more empty containers in which the goods can be loaded. Upon arrival at the destination, the goods are unloaded, and the empty containers must be transported to the pickup point for new customers. Therefore, NTS management needs to reallocate empty containers periodically (every week). The company's focus is on the transportation activity of empty containers, which is very expensive (almost 35% of the total operational costs). In May 2023, several empty containers, totaling 20 containers, need to be reallocated among terminals in Amsterdam, Berlin, Munich, Paris, Milan, Barcelona, and Madrid. The available or requested number of empty containers at various terminals is reported, along with the transportation costs (in euros per container) as seen in Figure 1.Determine how to solve the problem with the goal of minimizing…arrow_forwardDarren Mack owns the "Gas n' Go" convenience store and gas station. After hearing a marketing lecture, he realizes that it might be possible to draw more customers to his high-margin convenience store by selling his gasoline at a lower price. However, the "Gas n' Go' is unable to qualify for volume discounts on its gasoline purchases, and therefore cannot sell gasoline for profit if the price is lowered. Each new pump will cost $110,000 to install, but will increase customer traffic in the store by 11,000 customers per year. Also, because the "Gas n' Go" would be selling its gasoline at no profit, Darren plans on increasing the profit margin on convenience store items incrementally over the next five years. Assume a discount rate of 7 percent. The projected convenience store sales per customer and the projected profit margin for the next five years are given in the table below. i Year 1 2345 Projected Convenience Store Sales Per Customer $4 $5.50 $8 $10 $12 Projected Profit Margin 20%…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,