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 72P
Summary Introduction
To determine: The way to minimize the daily cost of transportation.
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 unfeasible solution.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Formulate 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
= 100
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…
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?
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
- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?arrow_forwardThe Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.arrow_forwardCompanies 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…arrow_forward
- 3.4-15* A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized below: Weight Саpacity (Tons) Space Сapacity (Cubic Feet) Compartment Front 7,000 9,000 5,000 12 Center 18 Back 10 Furthermore, the weight of the cargo in the respective compart- ments must be the same proportion of that compartment's weight capacity to maintain the balance of the airplane.arrow_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_forwardThe Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of delivering and transferring the fuel to MBC’s storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year; and the annual fuel usage is 150,000 gallons. MBC buses operate 300 days a year. a. What is the optimal order quantity for MBC? b. How frequently should MBC order to replenish the gasoline quantity? c. What is the reorder point?arrow_forward
- Darren 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_forwardQL (“Quebec Lumber”) is a logging and wood processing firm in a remote part of the Canadian province of Quebec. They have recently acquired a remote track of timber that is located ten miles from their processing facility. Normally, this is not a problem as they are able to simply cut the timber and haul it using trucks to their processing facility. However, this track of forestland is ten miles to their north, and there are no roads connecting the tract of land to their facility. They have also acquired a narrow (120 foot wide) ten-mile strip of land connecting this tract of timber to their processing facility. QL considered building their own road between the two points, and have log trucks haul the logs to the processing facility. However, they have decided instead to go with a less expensive option, a narrow gauge railroad. The narrow gauge railroad would require the laying of ties and steel tracks, and will require a custom-built locomotive and rolling stock (train cars that will…arrow_forwardThe Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of delivering and transferring the fuel to MBC’s storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year; and annual fuel usage is 150,000 gallons. MBC buses operate 300 days a year.a. What is the optimal quantity for MBC? b. how frequently should MBC order to replenish the gasoline supply? c. the MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expanding the capacity of its storage tanks? d. what is the recorder point?arrow_forward
- RVW (Restored Volkswagens) buys 15 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 10 to each of three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are costs associated with average repair expenses and transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost. Given the costs below, determine a minimum total cost schedule for RVW. Repair Shops Used Car Lots si S2 L1 L2 L3 Auction 1 550 500 s1 250 300 500 Auction 2 600 450 S2 350 650 450arrow_forwardThe Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $150 per order to cover the expenses of delivering and transferring the fuel to MBC's storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.02 per month, or $0.24 per year; and annual fuel usage is 180,000 gallons. MBC buses operate 288 days a year. (a) What is the optimal order quantity for MBC? (b) How frequently should MBC order to replenish The gasoline supply? -Select- per ---Select-- (c) The MBC storage tanks have a capacity of 17,500 gallons. Should MBC consider expanding the capacity of its storage tanks? The maximum inventory is (d) What is the reorder point (in gallons)? gallons Need Help? Read it Iddebat in MBC-Select-- ✓to expand its storage tanks.arrow_forwardThe Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $200 per order to cover the expenses of delivering and transferring the fuel to MBC's storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year; and annual fuel usage is 120,000 gallons. MBC buses operate 300 days a year. (a) What is the optimal order quantity for MBC? (b) How frequently should MBC order to replenish the gasoline supply? ---Select-- per ---Select--- (c) The MBC storage tanks have a capacity of 12,500 gallons. Should MBC consider expanding the capacity of its storage tanks? The maximum inventory is to expand its storage tanks. (d) What is the reorder point (in gallons)? gallons MBC --Select---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,