Find the Minimum Value of the Objective Function and Where

question 67

Multiple Choice

Find the minimum value of the objective function and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 4x + 16y
​
Constraints:
​
X ≥ 0
Y ≥ 0
2x + y ≤ 12​ ​

• A)Minimum at (0, 0): 0
• B)Minimum at (6, 0): 49
• C)Minimum at (0, 6): 48
• D)Minimum at (12, 0): 192
• E)Minimum at (0, 12): 193

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Definitions:

Double Declining Balance

An accelerated method of depreciation which doubles the rate at which an asset is depreciated compared to the straight-line method.

Straight-Line Method

This approach spreads the cost of a fixed asset evenly over its expected productive life, ensuring a consistent depreciation expense each year.

Impairment

A reduction in the recoverable value of an asset below its carrying amount on the balance sheet, reflecting a decline in the asset's utility.

Residual Value

The estimated value that an asset will have at the end of its useful life, often used in calculating depreciation.