To determine which combinations of coolers and radios Aruba could produce in one 40-hour week, we need to calculate the total labor hours required for each combination of production.
In Aruba:
- It takes 2 hours to make 1 cooler.
- It takes 5 hours to make 1 radio.
Now, let's analyze each option:
a. 5 coolers and 6 radios
- Labor for coolers: \(5 \text{ coolers} \times 2 \text{ hours/cooler} = 10 \text{ hours}\)
- Labor for radios: \(6 \text{ radios} \times 5 \text{ hours/radio} = 30 \text{ hours}\)
- Total labor: \(10 + 30 = 40 \text{ hours}\)
- This combination is feasible.
b. 13 coolers and 3 radios
- Labor for coolers: \(13 \text{ coolers} \times 2 \text{ hours/cooler} = 26 \text{ hours}\)
- Labor for radios: \(3 \text{ radios} \times 5 \text{ hours/radio} = 15 \text{ hours}\)
- Total labor: \(26 + 15 = 41 \text{ hours}\)
- This combination is not feasible (exceeds 40 hours).
c. 3 coolers and 7 radios
- Labor for coolers: \(3 \text{ coolers} \times 2 \text{ hours/cooler} = 6 \text{ hours}\)
- Labor for radios: \(7 \text{ radios} \times 5 \text{ hours/radio} = 35 \text{ hours}\)
- Total labor: \(6 + 35 = 41 \text{ hours}\)
- This combination is not feasible (exceeds 40 hours).
d. 11 coolers and 4 radios
- Labor for coolers: \(11 \text{ coolers} \times 2 \text{ hours/cooler} = 22 \text{ hours}\)
- Labor for radios: \(4 \text{ radios} \times 5 \text{ hours/radio} = 20 \text{ hours}\)
- Total labor: \(22 + 20 = 42 \text{ hours}\)
- This combination is not feasible (exceeds 40 hours).
Conclusion: The only combination of coolers and radios that Aruba can produce in one 40-hour week is option a: 5 coolers and 6 radios.
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