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 28,500 units of aluminum. The racing, touring, and mountain models need 11, 18, and 22 units of steel, and 12, 24, and 15 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 $9 per racing bike $11 per touring bike, and $23 per mountain bike? (b) What is the maximum possible profit? (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 variable.
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 28,500 units of aluminum. The racing, touring, and mountain models need 11, 18, and 22 units of steel, and 12, 24, and 15 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 $9 per racing bike $11 per touring bike, and $23 per mountain bike? (b) What is the maximum possible profit? (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 variable.
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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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 28,500 units of aluminum. The racing, touring, and mountain models need 11, 18,
and 22 units of steel, and 12, 24, and 15 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 $9 per racing bike
$11 per touring bike, and $23 per mountain bike?
(b) What is the maximum possible profit?
(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 variable.
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