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cturer of bicycles bullds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. Tne company nas avallable 39,600 units of steel and 34,200 units of aluminum. The racing, tourin 8, and 22 units of steel, and 12, 27, and 18 units of aluminum, respectively. Complete parts (a) through (d) below. a) How many of each type of bicycle should be made in order to maximize profit if the company makes $7 per racing bike, $11 per touring bike, and $20 per mountain bike? et x, be the number of racing bikes, let x, be the number touring bikes, and let x, be the number of mountain bikes. What is the objective function? == 7 x, + 11 x2 + 20 x3 Do not include the $ symbol in your answers.) o maximize profit, the company should produce 0 racing bike(s). O touring bike(s), and 1800 mountain bike(s). Simplify your answers.) b) What is the maximum possible profit? The maximum profit is $ 36000 Simplify your answer.) c) Does it require all of the available units of steel and aluminum to build the bicycles that produce the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. No. Since s, = and s, = in the optimal solution, there islare unit(s) of steel and unit(s) of aluminum, respectively, left over. (Simplify your answers.)

cturer of bicycles bullds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. Tne company nas avallable 39,600 units of steel and 34,200 units of aluminum. The racing, tourin 8, and 22 units of steel, and 12, 27, and 18 units of aluminum, respectively. Complete parts (a) through (d) below. a) How many of each type of bicycle should be made in order to maximize profit if the company makes $7 per racing bike, $11 per touring bike, and $20 per mountain bike? et x, be the number of racing bikes, let x, be the number touring bikes, and let x, be the number of mountain bikes. What is the objective function? == 7 x, + 11 x2 + 20 x3 Do not include the $ symbol in your answers.) o maximize profit, the company should produce 0 racing bike(s). O touring bike(s), and 1800 mountain bike(s). Simplify your answers.) b) What is the maximum possible profit? The maximum profit is $ 36000 Simplify your answer.) c) Does it require all of the available units of steel and aluminum to build the bicycles that produce the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. No. Since s, = and s, = in the optimal solution, there islare unit(s) of steel and unit(s) of aluminum, respectively, left over. (Simplify your answers.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 39,600 units of steel and 34,200 units of aluminum. The racing, touring, and mountain models need 11, 18, and 22 units of steel, and 12, 27, and 18 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $7 per racing bike, $11 per touring bike, and $20 per mountain bike? Let x, be the number of racing bikes, let x, be the number touring bikes, and let x, be the number of mountain bikes. What is the objective function? z= 7 x, + 11 x, + 20 x3 (Do not include the $ symbol in your answers.) To maximize profit, the company should produce 0 racing bike(s), 0 touring bike(s), and 1800 mountain bike(s). (Simplify your answers.) (b) What is the maximum possible profit? The maximum profit is $ 36000 . (Simplify your answer.) (c) Does it quire all of the available units of steel and aluminum to build the bicycle that the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack variable. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. No. Since s, = and s2 = in the optimal solution, there is/are unit(s) of steel and unit(s) of aluminum, respectively, left over. (Simplify your answers.) O B. Yes. All available units of steel and aluminum are required to build the optimal group of bicycles.
Transcribed Image Text:A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 39,600 units of steel and 34,200 units of aluminum. The racing, touring, and mountain models need 11, 18, and 22 units of steel, and 12, 27, and 18 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $7 per racing bike, $11 per touring bike, and $20 per mountain bike? Let x, be the number of racing bikes, let x, be the number touring bikes, and let x, be the number of mountain bikes. What is the objective function? z= 7 x, + 11 x, + 20 x3 (Do not include the $ symbol in your answers.) To maximize profit, the company should produce 0 racing bike(s), 0 touring bike(s), and 1800 mountain bike(s). (Simplify your answers.) (b) What is the maximum possible profit? The maximum profit is $ 36000 . (Simplify your answer.) (c) Does it quire all of the available units of steel and aluminum to build the bicycle that the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack variable. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. No. Since s, = and s2 = in the optimal solution, there is/are unit(s) of steel and unit(s) of aluminum, respectively, left over. (Simplify your answers.) O B. Yes. All available units of steel and aluminum are required to build the optimal group of bicycles.
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