Consider the Following Integer Programming Problem \mathrm    { Z } = 2 x _ { 1 } + x _ { 2 }

question 21

Multiple Choice

Consider the following integer programming problem. Solve it using the branch and bound method. What are the optimal values of x1, x2, and Z?
Maximize \mathrm    { Z } = 2 x _ { 1 } + x _ { 2 }
Subject to: \quad    2 x _ { 1 } + 2 x _ { 2 } \leq 7
           $4 x _ { 1 } + x _ { 2 } \leq 11$
             $x _ { 1 }$ and $x _ { 2 } \geq 0$

• A) x₁ = 1, x₂ = 2, Z = 4
• B) x₁= 2, x₂ = 1, Z = 5
• C) x₁ = 1, x₂ = 1, Z = 3
• D) x₁ = 0, x₂= 3, Z = 3
• E) x₁ = 2, x₂ = 2, Z = 6

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Definitions:

Discount Rate

The interest rate charged to commercial banks and other financial institutions for loans received from a country's central bank.

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The present worth of a future sum of money or series of cash flows, based on a given return rate.

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Cash Today refers to the availability of funds or capital that can be immediately used or invested, as opposed to future earnings or receivables.

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The augmentation or diminution in an investment's valuation across a specified timeframe, articulated as a fraction of the initial investment expense.