CBF Throughput accounting

Hello,

I have difficulty getting the working from the answer on one particular question in PM book from Kaplan. The question is as follows:

After each manufacture, each heater has to go through 3 processes: Assembly, Quality Control and Packaging. The following information is available for the 3 heaters:

Alpha Beta Gamma
Sales price per unit $2.0 $2.25 $1.75
Direct material cost per unit $0.50 $0.81 $0.35
Direct labour cost per unit $0.30 $0.60 $0.50
Machine time per unit:
Assembly (in minutes) 2 3 2.5
Quality Control (in minutes) 3 4 2
Packaging (in minutes) 4 5 3
Weekly sales demand (units) 1,000 1,500 850

Operating expenses, including labour, are $4,500. The maximum hours available for the machines are 150 hours (Assembly), 170 hours (Quality Control) and 250 hours (Packaging).

In first step i know i need to identify the bottleneck and to be able to do so i need to calculate the hours required for maximum production. Total demand would be 3,350 units (1,000 for Alpha + 1,500 for Beta + 850 for Gamma). The maximum machine hours available on Assembly are 150 hours (9,000 minutes). The time it takes to assemble all the units would be 7.5 minutes per unit (2 min. for Alpha + 3 min. for Beta + 2.5 min. for Gamma).

The answer given for Assembly hours needed for maximum production states 143.75 hours and i cannot come to this figure, however, I try. Similarly answer given for Quality Control and Packaging for hours needed for maximum production are: 178.33 and 234.17 respectively.

Would you be able to assist with the detail on how to approach the calculation for Assembly hours needed for maximum production?

Many thanks