A company manufactures and sells three types of doors: steel, wood, and aluminium. Labor, energy and capital requirements along with profit margins are reported in the following table: Steel Wood Aluminum Labor (Hours) 9 12 8 Energy (Units) 20 14 16 Capital ($) 90 50 70 Profit Margin ($) 45 35 52 The manager of the company has decided to sell more wood doors than the combined total steel and aluminum doors sold. Due to demand constraint, steel doors sold cannot exceed 30. The company has available 600 hours of labor, 450 units of energy and $40,000 of capital. The objective of the company is to maximize total profit.

Practical Management Science
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A company manufactures and sells three types of doors: steel, wood, and aluminium.
Labor, energy and capital requirements along with profit margins are reported in the
following table:
Steel
Wood
Aluminum
Labor
(Hours)
9
12
8
Energy
(Units)
20
14
16
Capital
($)
90
50
70
Profit Margin
($)
45
35
52
The manager of the company has decided to sell more wood doors than the combined
total steel and aluminum doors sold. Due to demand constraint, steel doors sold cannot
exceed 30. The company has available 600 hours of labor, 450 units of energy and
$40,000 of capital. The objective of the company is to maximize total profit.
1. Identify the decision variables.
2.
Identify and formulate the objective function.
3. Identify and formulate the constraints.
4. Formulate the above business problem as a Linear Programming Model.
Transcribed Image Text:A company manufactures and sells three types of doors: steel, wood, and aluminium. Labor, energy and capital requirements along with profit margins are reported in the following table: Steel Wood Aluminum Labor (Hours) 9 12 8 Energy (Units) 20 14 16 Capital ($) 90 50 70 Profit Margin ($) 45 35 52 The manager of the company has decided to sell more wood doors than the combined total steel and aluminum doors sold. Due to demand constraint, steel doors sold cannot exceed 30. The company has available 600 hours of labor, 450 units of energy and $40,000 of capital. The objective of the company is to maximize total profit. 1. Identify the decision variables. 2. Identify and formulate the objective function. 3. Identify and formulate the constraints. 4. Formulate the above business problem as a Linear Programming Model.
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