Question

A company manufactures three models of bicycles: A, B, and C. Each bicycle passes through three departments: fabrication, painting and plating, and final assembly. Bicycle A requires 3 hours in fabrication, 5 hours in painting and plating, and 4 hours in final assembly. Bicycle B requires 4 hours in fabrication, 3 hours in painting and plating, and 3 hours in final assembly. Bicycle C requires 5 hours in fabrication, 5 hours in painting and plating, and 5 hours in final assembly. The maximum labor hours available per day are 120 hours in fabrication, 130 hours in painting and plating, and 140 hours in final assembly. If the profit per bicycle is $80 for bicycle A, $70 for bicycle B, and $100 for bicycle C, how many bicycles of models A, B, and C must be sold to maximize the profit? a) Define the variables and set up the linear program used to maximize profit. DO NOT solve the linear program. b) Give the initial simplex table for the linear program and circle the first pivot. DO NOT solve the linear program. Below is the final simplex table corresponding to the linear program. Use the table to answer the following questions. [1 0 0 0 | 10 10 0 | 2500] [0 0 11 10 | 5 -3 0 | 210] [0 2 -1 0 | -1 1 0 | 10] [0 0 1 0 | 1 1 -2 | -30] c) What is the maximum profit? d) How many bicycles of model A, B, and C should be sold to maximize the profit? e) When profit is maximized, how many hours of labor in each department go unused?

          A company manufactures three models of bicycles: A, B, and C. Each bicycle passes through three departments: fabrication, painting and plating, and final assembly. Bicycle A requires 3 hours in fabrication, 5 hours in painting and plating, and 4 hours in final assembly. Bicycle B requires 4 hours in fabrication, 3 hours in painting and plating, and 3 hours in final assembly. Bicycle C requires 5 hours in fabrication, 5 hours in painting and plating, and 5 hours in final assembly. The maximum labor hours available per day are 120 hours in fabrication, 130 hours in painting and plating, and 140 hours in final assembly. If the profit per bicycle is $80 for bicycle A, $70 for bicycle B, and $100 for bicycle C, how many bicycles of models A, B, and C must be sold to maximize the profit?

a) Define the variables and set up the linear program used to maximize profit. DO NOT solve the linear program.
b) Give the initial simplex table for the linear program and circle the first pivot. DO NOT solve the linear program.

Below is the final simplex table corresponding to the linear program. Use the table to answer the following questions.

[1 0 0 0 | 10 10 0 | 2500]
[0 0 11 10 | 5 -3 0 | 210]
[0 2 -1 0 | -1 1 0 | 10]
[0 0 1 0 | 1 1 -2 | -30]

c) What is the maximum profit?
d) How many bicycles of model A, B, and C should be sold to maximize the profit?
e) When profit is maximized, how many hours of labor in each department go unused?

A company manufactures three models of bicycles: A, B, and C. Each bicycle passes through three departments: fabrication, painting and plating, and final assembly. Bicycle A requires 3 hours in fabrication, 5 hours in painting and plating, and 4 hours in final assembly. Bicycle B requires 4 hours in fabrication, 3 hours in painting and plating, and 3 hours in final assembly. Bicycle C requires 5 hours in fabrication, 5 hours in painting and plating, and 5 hours in final assembly. The maximum labor hours available per day are 120 hours in fabrication, 130 hours in painting and plating, and 140 hours in final assembly. If the profit per bicycle is 80 for bicycle A,70 for bicycle B, and 100 for bicycle C, how many bicycles of models A, B, and C must be sold to maximize the profit?

a) Define the variables and set up the linear program used to maximize profit. DO NOT solve the linear program.
b) Give the initial simplex table for the linear program and circle the first pivot. DO NOT solve the linear program.

Below is the final simplex table corresponding to the linear program. Use the table to answer the following questions.

[1 0 0 0 | 10 10 0 | 2500]
[0 0 11 10 | 5 -3 0 | 210]
[0 2 -1 0 | -1 1 0 | 10]
[0 0 1 0 | 1 1 -2 | -30]

c) What is the maximum profit?
d) How many bicycles of model A, B, and C should be sold to maximize the profit?
e) When profit is maximized, how many hours of labor in each department go unused?

Added by Courtney W.

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