Question

work and required resources
intermountain factory has a job that is going to take 70 days of work to complete. which of the following combinations will give them enough days of work to finish the job?
will this combination work?
yes no 3 people working for 20 days
yes no 2 people working for 25 days and 4 people working for 5 days
yes no 9 people working for 4 days and 2 people working for 16 days
yes no 4 people working for 18 days
yes no 1 person working for 70 days
yes no 70 people working for 1 day
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Explanation:

Step1: Calculate total work days

Total required work days = $70$ person-days

Step2: Evaluate 1st combination

Calculate total work: $3 \times 20 = 60$ person-days

Step3: Evaluate 2nd combination

Calculate total work: $(2 \times 25) + (4 \times 5) = 50 + 20 = 70$ person-days

Step4: Evaluate 3rd combination

Calculate total work: $(9 \times 4) + (2 \times 16) = 36 + 32 = 68$ person-days

Step5: Evaluate 4th combination

Calculate total work: $4 \times 18 = 72$ person-days

Step6: Evaluate 5th combination

Calculate total work: $1 \times 70 = 70$ person-days

Step7: Evaluate 6th combination

Calculate total work: $70 \times 1 = 70$ person-days

Step8: Compare to required work

A combination works if total $\geq 70$ person-days

Answer:

1. 3 people working for 20 days: No
2. 2 people working for 25 days and 4 people working for 5 days: Yes
3. 9 people working for 4 days and 2 people working for 16 days: No
4. 4 people working for 18 days: Yes
5. 1 person working for 70 days: Yes
6. 70 people working for 1 day: Yes