A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 91,800 units of steel and 42,000 units of aluminum. The racing, touring, and mountain models need 17, 27, and 34 units of steel, and 12, 21, and 15 units of aluminum, respectively. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 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.
set up and solve using the by the simplex method.
A manufacturer of bicycles builds racing, touring, and mountain models. The
bicycles are made of both steel and aluminum. The company
has available 91,800 units of steel and 42,000 units of aluminum.
The racing, touring, and mountain models need 17, 27, and
34 units of steel, and 12, 21, and 15 units of aluminum, respectively.
(a) How many of each type of bicycle should be made in order
to maximize profit if the company makes $8 per racing
bike, $12 per touring bike, and $22 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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