To determine which combinations Zimbabwe cannot produce in 120 minutes, we first need to calculate the total time needed to produce each combination based on the machine minutes required for each product.
Zimbabwe's machine minutes:
- Toothbrush: 3 minutes each
- Hairbrush: 10 minutes each
Let's calculate the total time required for each option:
a. 10 toothbrushes and 9 hairbrushes
- Time for toothbrushes: 10 toothbrushes * 3 minutes/toothbrush = 30 minutes
- Time for hairbrushes: 9 hairbrushes * 10 minutes/hairbrush = 90 minutes
- Total time: 30 + 90 = 120 minutes
b. 5 toothbrushes and 11 hairbrushes
- Time for toothbrushes: 5 toothbrushes * 3 minutes/toothbrush = 15 minutes
- Time for hairbrushes: 11 hairbrushes * 10 minutes/hairbrush = 110 minutes
- Total time: 15 + 110 = 125 minutes
c. 20 toothbrushes and 6 hairbrushes
- Time for toothbrushes: 20 toothbrushes * 3 minutes/toothbrush = 60 minutes
- Time for hairbrushes: 6 hairbrushes * 10 minutes/hairbrush = 60 minutes
- Total time: 60 + 60 = 120 minutes
d. 30 toothbrushes and 3 hairbrushes
- Time for toothbrushes: 30 toothbrushes * 3 minutes/toothbrush = 90 minutes
- Time for hairbrushes: 3 hairbrushes * 10 minutes/hairbrush = 30 minutes
- Total time: 90 + 30 = 120 minutes
Now, let's summarize the findings:
- a. 10 toothbrushes and 9 hairbrushes: 120 minutes (can produce)
- b. 5 toothbrushes and 11 hairbrushes: 125 minutes (cannot produce)
- c. 20 toothbrushes and 6 hairbrushes: 120 minutes (can produce)
- d. 30 toothbrushes and 3 hairbrushes: 120 minutes (can produce)
Based on these calculations, the combination that Zimbabwe could not produce in 120 minutes is:
b. 5 toothbrushes and 11 hairbrushes.