Transporting Coal. The Calcio Coal Company produces coal at four mines and ships it to four power plants (P1-P4). The cost per ton of producing coal and the production capacity (in tons) for wach mine are known. The number of tons of each coal demanded by each customer is also known. The cost (in dollars) of shipping a ton of coal from a mine to each plant is available as well. The following table provides the data: P1 P2 P3 P4 Capacity Cost Mine 1 9 15 8 10 125 50 Mine 2 7 15 14 12 100 57 Mine 3 5 5 11 12 150 55 Mine 4 3 6 8 11 120 61 Demands 110 115 135 130 a. Calcio wishes to minimize the cost of transporting coal from its mines to its plants. What is the minimum cost? b. What is the transportation schedule that achieves the minimum cost in (a)? Note:-

Transporting Coal. The Calcio Coal Company produces coal at four mines and ships it to four power plants (P1-P4). The cost per ton of producing coal and the production capacity (in tons) for wach mine are known. The number of tons of each coal demanded by each customer is also known. The cost (in dollars) of shipping a ton of coal from a mine to each plant is available as well. The following table provides the data: P1 P2 P3 P4 Capacity Cost Mine 1 9 15 8 10 125 50 Mine 2 7 15 14 12 100 57 Mine 3 5 5 11 12 150 55 Mine 4 3 6 8 11 120 61 Demands 110 115 135 130 a. Calcio wishes to minimize the cost of transporting coal from its mines to its plants. What is the minimum cost? b. What is the transportation schedule that achieves the minimum cost in (a)? Note:-

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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The 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.
Cargo Loading. You are in charge of loading cargo ships for International Cargo Company (ICC) at a major East Coast port. You have been asked to prepare a loading plan for an ICC freighter bound for Africa. An agricultural commodities dealer would like to transport the following products aboard this ship:Commodity Tons Available Volume per Ton (cu.ft.) Profit per Ton ($)1 4,000 40 702 3,000 25 503 2,000 60 604 1,000 50 80You can elect to load any or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions: Cargo Hold Weight Capacity (tons) Volume Capacity (cu.ft.)Forward 3,000 100,000Center 5,000 150,000Rear 2,000 120,000More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10 percent of the weight in the rear cargo hold, and the center cargo hold…
Cargo Loading. You are in charge of loading cargo ships for International Cargo Company (ICC) at a major East Coast port. You have been asked to prepare a loading plan for an ICC freighter bound for Africa. An agricultural commodities dealer would like to transport the following products aboard this ship:Commodity Tons Available Volume per Ton (cu.ft.) Profit per Ton ($)1 4,000 40 702 3,000 25 503 2,000 60 604 1,000 50 80You can elect to load any or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions: Cargo Hold Weight Capacity (tons) Volume Capacity (cu.ft.)Forward 3,000 100,000Center 5,000 150,000Rear 2,000 120,000More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10 percent of the weight in the rear cargo hold, and the center cargo hold…
Suppliers A, B, and C supply components to three plants -- F, G, and H via two transshipment facilities -- T1 and T2. It costs $4 to ship from T1 regardless of final destination and $3 to ship to T2 regardless of supplier. Shipping to T1 from A, B, and C costs $3, $4, and $5, respectively, and shipping from T2 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. The Logistics Manager has come to you for help. Answer the following question: Which of these is not an element of the objective function? Group of answer choices 4D-T1 600T1 9T2-G 3C-T2 Plz do fast asap
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…
4. 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?
A seafood distribution company specializes in delivering fresh lobsters from their harvesting sites to various restaurants across the coastline. The company operates a fleet of sailing vessels, each with different capacities and operational costs. Due to the perishable nature of lobsters, the company aims to optimize its distribution network to minimize total costs while meeting the demand of each restaurant. Given Data: Sailing Vessels (with capacities and fixed operational costs): Vessel 1 (V1): Capacity = 300 kg, Fixed Cost = $1,000 Vessel 2 (V2): Capacity = 200 kg, Fixed Cost = $900 Vessel 3 (V3): Capacity = 400 kg, Fixed Cost = $1,200 Vessel 4 (V4): Capacity = 100 kg, Fixed Cost = $600 Restaurants (with lobster demand): Restaurant A: Demand = 250 kg Restaurant B: Demand = 150 kg Restaurant C: Demand = 300 kg Restaurant D: Demand = 100 kg Transportation Costs (per kg) from Harvesting Sites to Restaurants: Restaurant A…
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.
Radiant wants to hire Cargo planes for transporting their goods. They contacted VIP Transportation Company to hire Cargo planes. VIP informed that they can provide two types of Cargo Planes. In addition, they provided the following cost related information about the two types Cargo planes- WT88 and BH54: Personnel Cost Fuel Cost Maintenance Cost WT88 2000 1000 2000 BH54 2500 1500 1000 Radiant has $200,000 to spend in personnel cost, $160,000 in fuel cost, and $80,000 in maintenance cost. Moreover, they have to hire at least two of each type of planes. If WT88 can carry 55 tons of goods and BH54 can carry 85 tons of goods, then find out the following using Linear Programming: What is the maximum amount Radiant can carry given their budget constraint? Can you solve using solver ? (I did this but I got a wrong answer) Data Personnel Cost Fuel Cost Maintenance Cost Tons WT88 2000 1000 2000 55…
She must travel to Kenya to check on quality and transportation. The trip will cost $2,500. The cost of the handbag is $10 and shipping to the United States can occur through the postal system for $2 per handbag or through a freight company which will ship a container that can hold up to 1,000 handbags at a cost of $1,000. The freight company charges $1,000 even if less than 1,000 handbags are shipped. Leslie will sell the handbags to retailers for $20. Assume there are no other costs and benefits. what is the output level that both shipping methods yield same profit? Ho
A firm has established a distribution network for the supply of a raw material critical to itsmanufacturing. Currently there are two origins for this material, which must be shipped to threemanufacturing plants. The current network has the following characteristics: COSTS PLANT 1 PLANT 2 PLANT 3 SUPPLY Raw Material source 1 $6 $8 $9 400 Raw Material source 2 $4 $7 $3 600 Demand 500 500 500 Supply < Demand The firm has identified two potential sites for a third raw material source; these are identified asCandidate A and Candidate B. From A, the costs to ship would be $9 to Plant 1, $10 to Plant 2,and $12 to Plant 3. From B, these costs would be $11, $14, and $8. The new source, wherever itis located, will have a capacity of 500 units. Solve with the transportation method. Which siteshould be selected?
The 3J Company manufactures handbags, shoulder bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the daily availability of the resources, their usage by the three products, and the prices per unit. Leather (ft²) Sewing (hr) Finishing (hr) Price in Pesos Hand bag 3 2 2 1200 Requirement per Unit Shoulder bag 2 1.5 1 1100 Backpack 4 3 2 2250 Availability 45 43 47 a. Define the decision variables and formulate a linear programming model for this problem. b. Find the optimal solution using the Excel Solver and interpret the result. c. Determine the binding constraints. d. Consider an independent case for each decision variable. Find the range of prices for handbag, shoulder bag and backpack that makes the optimal solution remain unchanged. e. Determine the new optimal solution when the available…