Question

8. A toy manufacturer specializes in making a very popular plastic toy. The company wants to install sufficient equipment capacity so as to be able to produce 300,000 good units of the toy every year. The manufacturing operation takes about 5 minutes, but that model of machine has been known to have malfunctions periodically resulting in 2% defective outputs Each machine can be run for 2000 hours per year (taking into account the number of working days of the company and downtime for machine upkeep and maintenance). How many machines should the company buy?

Answer 1

Answer:
Annual requirement (in units) per year = 300,000

Time required to produce 1 unit = 5 min
Production machine Running hours per year = 2000 hrs = 2000 * 60 = 120000
Number of plastic toy units a machine can churn out every year = 120000 / 5 = 24000

Defect rate = 2%
=> Defective pieces produced out of 24000 units = 24000 * 2 / 100 = 480 units

So, Net yearly plastic toy units production of a single machine = 24000 - 480 = 23520

Hence total number of machines required to produce 300,000
= 300,000 / (Net yearly plastic toy units production of a single machine)
= 300,000 / 23520 = 12.755

The company should by 13 machines to meet the annual plastic toy production target.