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Question 1 A coffee company operates coffee roasters at 2 different acilities in the city. They have been contracted to supply 4 different restaurants with offee. Suppose that each restaurant requires 100 kg of coffee, and that Roasters 1 and have 180 kg and 220 kg, respectively, of coffee available for shipment each week. (a) Suppose that the cost in pounds of shipping each kg of coffee between the roaster and restaurants is as follows: Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Roaster 1 1.10 1.30 2.50 0.90 Roaster 2 1.50 1.75 1.20 1.25 Give a linear program to find the cheapest way for the company to fulfil its weekly shipping contract. State what each of the variables and constraints in you program represent. You do not need to solve this program. (b) The coffee company wants to know how to improve its shipping costs by increasing the amount of coffee available at one of the roasters. Suppose you had an optimal solution for your linear program for the previous question. Explain how you could determine how a small increase in the amount of coffee available a one of the roasters would affect the cost of the optimal solution without solving the program again. (c) Suppose now that the company is not concerned with shipping costs but instead wants to purchase some standard packaging for its shipments. It wants to send each shipment from a roaster to a restaurant in a single box. Suppose that these boxes are identical and each can hold at most some total weight w. The compan wants to know the smallest w required so that it can carry out its shipments in this way. Give a linear program to find this capacity. You do not need to solve this program.

Question 1 A coffee company operates coffee roasters at 2 different acilities in the city. They have been contracted to supply 4 different restaurants with offee. Suppose that each restaurant requires 100 kg of coffee, and that Roasters 1 and have 180 kg and 220 kg, respectively, of coffee available for shipment each week. (a) Suppose that the cost in pounds of shipping each kg of coffee between the roaster and restaurants is as follows: Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Roaster 1 1.10 1.30 2.50 0.90 Roaster 2 1.50 1.75 1.20 1.25 Give a linear program to find the cheapest way for the company to fulfil its weekly shipping contract. State what each of the variables and constraints in you program represent. You do not need to solve this program. (b) The coffee company wants to know how to improve its shipping costs by increasing the amount of coffee available at one of the roasters. Suppose you had an optimal solution for your linear program for the previous question. Explain how you could determine how a small increase in the amount of coffee available a one of the roasters would affect the cost of the optimal solution without solving the program again. (c) Suppose now that the company is not concerned with shipping costs but instead wants to purchase some standard packaging for its shipments. It wants to send each shipment from a roaster to a restaurant in a single box. Suppose that these boxes are identical and each can hold at most some total weight w. The compan wants to know the smallest w required so that it can carry out its shipments in this way. Give a linear program to find this capacity. You do not need to solve this program.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 24CT
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Question 1 facilities in the city. They have been contracted to supply 4 different restaurants with coffee. Suppose that each restaurant requires 100 kg of coffee, and that Roasters 1 and 2 have 180 kg and 220 kg, respectively, of coffee available for shipment each week. A coffee company operates coffee roasters at 2 different (a) Suppose that the cost in pounds of shipping each kg of coffee between the roasters and restaurants is as follows: Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Roaster 1 1.10 1.30 2.50 0.90 Roaster 2 1.50 1.75 1.20 1.25 Give a linear program to find the cheapest way for the company to fulfil its weekly shipping contract. State what each of the variables and constraints in your program represent. You do not need to solve this program. (b) The coffee company wants to know how to improve its shipping costs by increasing the amount of coffee available at one of the roasters. Suppose you had an optimal solution for your linear program for the previous question. Explain how you could determine how a small increase in the amount of coffee available at one of the roasters would affect the cost of the optimal solution without solving the program again. (c) Suppose now that the company is not concerned with shipping costs but instead wants to purchase some standard packaging for its shipments. It wants to send each shipment from a roaster to a restaurant in a single box. Suppose that these boxes are identical and each can hold at most some total weight w. The company wants to know the smallest w required so that it can carry out its shipments in this way. Give a linear program to find this capacity. You do not need to solve this program.
Transcribed Image Text:Question 1 facilities in the city. They have been contracted to supply 4 different restaurants with coffee. Suppose that each restaurant requires 100 kg of coffee, and that Roasters 1 and 2 have 180 kg and 220 kg, respectively, of coffee available for shipment each week. A coffee company operates coffee roasters at 2 different (a) Suppose that the cost in pounds of shipping each kg of coffee between the roasters and restaurants is as follows: Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Roaster 1 1.10 1.30 2.50 0.90 Roaster 2 1.50 1.75 1.20 1.25 Give a linear program to find the cheapest way for the company to fulfil its weekly shipping contract. State what each of the variables and constraints in your program represent. You do not need to solve this program. (b) The coffee company wants to know how to improve its shipping costs by increasing the amount of coffee available at one of the roasters. Suppose you had an optimal solution for your linear program for the previous question. Explain how you could determine how a small increase in the amount of coffee available at one of the roasters would affect the cost of the optimal solution without solving the program again. (c) Suppose now that the company is not concerned with shipping costs but instead wants to purchase some standard packaging for its shipments. It wants to send each shipment from a roaster to a restaurant in a single box. Suppose that these boxes are identical and each can hold at most some total weight w. The company wants to know the smallest w required so that it can carry out its shipments in this way. Give a linear program to find this capacity. You do not need to solve this program.
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