A manufacturer of bicycles builds 1-, 3- and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 43,800 units of steel and 55,450 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 12, 16 and 20 units of steel and 20, 15, and 25 units of aluminum. The company makes $3 per 1-speed bike, $4 per 3-speed, and $10 per 10-speed. Use the simplex method to complete parts (a) and (b). (a) How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x,, x,, and x, represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let z be the total profit. Z= subject to 12x, + 16x2 + 20x3 20x, + 15x2 + 25x3 X1 20, X2 20, x3 20. (Do not factor. Do not include the $ symbol in your answers.)
A manufacturer of bicycles builds 1-, 3- and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 43,800 units of steel and 55,450 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 12, 16 and 20 units of steel and 20, 15, and 25 units of aluminum. The company makes $3 per 1-speed bike, $4 per 3-speed, and $10 per 10-speed. Use the simplex method to complete parts (a) and (b). (a) How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x,, x,, and x, represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let z be the total profit. Z= subject to 12x, + 16x2 + 20x3 20x, + 15x2 + 25x3 X1 20, X2 20, x3 20. (Do not factor. Do not include the $ symbol in your answers.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Bicycle Production Optimization Problem**
A manufacturer of bicycles builds 1-, 3-, and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 43,800 units of steel and 55,450 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 12, 16, and 20 units of steel and 20, 15, and 25 units of aluminum. The company makes $3 per 1-speed bike, $4 per 3-speed, and $10 per 10-speed. Use the simplex method to complete parts (a) and (b).
**(a)** How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit?
Set up the linear programming problem. Let \( x_1, x_2, \) and \( x_3 \) represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let \( z \) be the total profit.
Maximize:
\[ z = \underline{\hspace{2cm}} \]
subject to:
\[ 12x_1 + 16x_2 + 20x_3 \leq \underline{\hspace{2cm}} \]
\[ 20x_1 + 15x_2 + 25x_3 \leq \underline{\hspace{2cm}} \]
\[ x_1 \geq 0, \, x_2 \geq 0, \, x_3 \geq 0 \]
(Do not factor. Do not include the $ symbol in your answers.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9ef355a-fb22-427b-b06e-27c19f3d746c%2F609c135a-bb4f-4adc-9132-ef20b7468a1c%2Faq6kuq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Bicycle Production Optimization Problem**
A manufacturer of bicycles builds 1-, 3-, and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 43,800 units of steel and 55,450 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 12, 16, and 20 units of steel and 20, 15, and 25 units of aluminum. The company makes $3 per 1-speed bike, $4 per 3-speed, and $10 per 10-speed. Use the simplex method to complete parts (a) and (b).
**(a)** How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit?
Set up the linear programming problem. Let \( x_1, x_2, \) and \( x_3 \) represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let \( z \) be the total profit.
Maximize:
\[ z = \underline{\hspace{2cm}} \]
subject to:
\[ 12x_1 + 16x_2 + 20x_3 \leq \underline{\hspace{2cm}} \]
\[ 20x_1 + 15x_2 + 25x_3 \leq \underline{\hspace{2cm}} \]
\[ x_1 \geq 0, \, x_2 \geq 0, \, x_3 \geq 0 \]
(Do not factor. Do not include the $ symbol in your answers.)
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