Question

lisa needs to arrive in ankara from istanbul in the next 5 hours. she wants to save as much money as possible, while minimizing her travel time to allow for more sightseeing. she looks at the local transportation options and determines the possibilities for that particular day in the table.

\

$$\begin{tabular}{|c|c|c|} \\hline transportation & cost & travel time \\\\ \\hline bus & \\$16.30 & 6 hours \\\\ \\hline rental car & \\$51.40 & 5 hours \\\\ \\hline train & \\$11.70 & 1.5 hours \\\\ \\hline airplane & \\$60.70 & 1 hour \\\\ \\hline \\end{tabular}$$

which mode of transportation should lisa choose if she wants to minimize her cost and maximize her sightseeing time?

a. bus
b. rental car
c. train
d. airplane

Explanation:

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<reasoning>

Identify constraints and objectives

Using the Table Reading knowledge point

• Time constraint: Travel time must be at most 5 hours (\(t \le 5\)).
• Primary objective: Minimize cost.
• Secondary objective: Maximize sightseeing time (which means minimizing travel time).

Filter options by time constraint

Using the Table Reading knowledge point

• Bus: 6 hours (Invalid, exceeds 5 hours)
• Rental Car: 5 hours (Valid)
• Train: 1.5 hours (Valid)
• Airplane: 1 hour (Valid)

Compare cost of valid options

Using the Cost Minimization knowledge point

• Rental Car: \(\$51.40\)
• Train: \(\$11.70\)
• Airplane: \(\$60.70\)

The option with the lowest cost among the valid choices is the Train at \(\$11.70\).

Evaluate secondary objective

Using the Cost Minimization knowledge point

• The Train costs \(\$11.70\) and takes 1.5 hours.
• The Train is both the cheapest valid option and has a very short travel time (1.5 hours), which maximizes sightseeing time compared to the rental car (5 hours).
• Therefore, the Train is the optimal choice.

</reasoning>

<answer>
<mcq-option>a. bus</mcq-option>
<mcq-option>b. rental car</mcq-option>
<mcq-correct>c. train</mcq-correct>
<mcq-option>d. airplane</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify constraints and objectives

Using the Table Reading knowledge point

• Time constraint: Travel time must be at most 5 hours (\(t \le 5\)).
• Primary objective: Minimize cost.
• Secondary objective: Maximize sightseeing time (which means minimizing travel time).

Filter options by time constraint

Using the Table Reading knowledge point

• Bus: 6 hours (Invalid, exceeds 5 hours)
• Rental Car: 5 hours (Valid)
• Train: 1.5 hours (Valid)
• Airplane: 1 hour (Valid)

Compare cost of valid options

Using the Cost Minimization knowledge point

• Rental Car: \(\$51.40\)
• Train: \(\$11.70\)
• Airplane: \(\$60.70\)

The option with the lowest cost among the valid choices is the Train at \(\$11.70\).

Evaluate secondary objective

Using the Cost Minimization knowledge point

• The Train costs \(\$11.70\) and takes 1.5 hours.
• The Train is both the cheapest valid option and has a very short travel time (1.5 hours), which maximizes sightseeing time compared to the rental car (5 hours).
• Therefore, the Train is the optimal choice.

</reasoning>

<answer>
<mcq-option>a. bus</mcq-option>
<mcq-option>b. rental car</mcq-option>
<mcq-correct>c. train</mcq-correct>
<mcq-option>d. airplane</mcq-option>
</answer>

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