Question

Which of the following combinations of toothbrushes and hairbrushes could Zimbabwe not produce in 120 minutes?

a) 20 toothbrushes, 30 hairbrushes
b) 30 toothbrushes, 20 hairbrushes
c) 25 toothbrushes, 25 hairbrushes
d) 40 toothbrushes, 10 hairbrushes

Answer 1

To determine the combination Zimbabwe could not produce in 120 minutes, we need to calculate the total production time for each combination of toothbrushes and hairbrushes.

Step-by-step explanation:

To solve this problem, we need to calculate the total time it takes to produce each combination of toothbrushes and hairbrushes. The time it takes to produce one toothbrush is exponentially distributed with a mean of minutes, and the time it takes to produce one hairbrush is also exponentially distributed with the same mean.

1. a) 20 toothbrushes, 30 hairbrushes: Total time = (20 toothbrushes) * (mean time per toothbrush) + (30 hairbrushes) * (mean time per hairbrush).
2. b) 30 toothbrushes, 20 hairbrushes: Total time = (30 toothbrushes) * (mean time per toothbrush) + (20 hairbrushes) * (mean time per hairbrush).
3. c) 25 toothbrushes, 25 hairbrushes: Total time = (25 toothbrushes) * (mean time per toothbrush) + (25 hairbrushes) * (mean time per hairbrush).
4. d) 40 toothbrushes, 10 hairbrushes: Total time = (40 toothbrushes) * (mean time per toothbrush) + (10 hairbrushes) * (mean time per hairbrush).

Then, we can compare the total time for each combination to 120 minutes to determine which combination Zimbabwe could not produce.