A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 98,600 units of steel and 45,000 units of aluminum. The racing, touring, and mountain models need 17, 29, and 34 units of steel, and 9, 24, and 15 units of aluminum, respectively Complete parts (a) through (d) below. C (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $9 per racing bike, $12 per touring bike, and $23 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-9x, +12x,+23 x, (Do not include the $ symbol in your answers.) To maximize profit, the company should produce racing bike(s). touring bike(s), and mountain bike(s). (Simplity your answers.) (b) What is the maximum possible profit? The maximum profit is S (Simplify your answer) (c) Doos 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. 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 is/are unit(s) of steel and unit(s) of aluminum, respectively, left over. ARMIMH
A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 98,600 units of steel and 45,000 units of aluminum. The racing, touring, and mountain models need 17, 29, and 34 units of steel, and 9, 24, and 15 units of aluminum, respectively Complete parts (a) through (d) below. C (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $9 per racing bike, $12 per touring bike, and $23 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-9x, +12x,+23 x, (Do not include the $ symbol in your answers.) To maximize profit, the company should produce racing bike(s). touring bike(s), and mountain bike(s). (Simplity your answers.) (b) What is the maximum possible profit? The maximum profit is S (Simplify your answer) (c) Doos 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. 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 is/are unit(s) of steel and unit(s) of aluminum, respectively, left over. ARMIMH
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 58P
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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 98,600 units
of steel and 45,000 units of aluminum. The racing, touring, and mountain models need 17, 29, and 34 units of steel, and 9, 24, and 15 units of aluminum, respectively
Complete parts (a) through (d) below.
(a) How many of each fype of bicycle should be made in order to maximize profit if the company makes $9 per racing bike, $12 per touring bike, and $23 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-9x, +12x, 23x
(Do not include the $ symbol in your answers.)
To maximize profit, the company should produce racing bike(s). touring bike(s), and mountain bike(s).
(Simplity your answers.)
(b) What is the maximum possible profit?
The maximum profit is S
(Simplify your answer.)
(c) Doos it require all of the available units of steel and aluminum to buld 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 rolevant slack variable.
Select the correct choice below and, if necessary, fil in the answer boxes to complete your choice
O A. No. Since s,
and s,
in the optimal solution, there is/are unit(s) of steel and unit(s) of aluminum, respectively, left over.
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