BPP Question. Bottleneck and TPAR

MN Co Manufactures automated industrial trolleys. Each Trolley sells for $2,000 and the material cost per unit is $600. Labour and variable overhead are $5,500 and $8,000 per week respectively. Fixed production costs are $450,000 per year and marketing and administrative cost are $265,000 per year.

MN Co manufactures automated industrial trolleys. Each trolley sells for $2,000, and the material cost per unit is $600. Labour costs are $5,500 per week, and variable overheads are $8,000 per week. Fixed production costs amount to $450,000 per year, and marketing and administrative costs are $265,000 per year.

MN Co manufactures automated industrial trolleys. Each trolley sells for $2,000, and the material cost per unit is $600. Labour costs are $5,500 per week, and variable overheads are $8,000 per week. Fixed production costs amount to $450,000 per year, and marketing and administrative costs are $265,000 per year.

The trolleys are made on three different machines. Machine X makes four frame panels required for each trolley. Its maximum output is 180 frame panels per week. Machine X is old and unreliable and it breaks down from time to time. It is estimated that 20 hours of production are lost per month. Machine Y can manufacture parts for 52 trolleys per week and machine Z, which is old but reasonably reliable, can process and assemble 30 trolleys per week.

The company has recently introduced a just-in-time (JIT) system and it is company policy to hold little work in progress and no finished goods inventory from week to week. The company operates a 40-hour week, 48 weeks a year.

Which is the bottleneck machine?

Answer:

Machine X loses 20 hours/ mth = 5 hours / week
loss of 12.5%
Max output of panels is hence 180 – 12.5% = 158
No. of trolleys = panels/4 = 39

Please can you explain where 12.5% comes from and how is 180 – 12.5% equal to 158?