F5 – Theory of Constraints

Hi, Could you please help me with one quick query on the below question with solution? Having tough time figuring it out, sure am missing something. How in the world do we arrive at Additional Sales from current position, for example: Buy C & B is getting additional sales of 150 units; buying C, B&A is getting additional sales of 250 units? Appreciate your help!

Example 1 – Theory of constraints
Demand for a product made by P Ltd is 500 units per week. The product is made in three consecutive processes – A, B, and C. Process capacities are:

Process

A

B

C

Capacity per week

400

300

250

The long-run benefit to P Ltd of increasing sales of its product is a present value of $25,000 per additional unit sold per week.

Investigations have revealed the following possibilities:

(1) Invest in a new machine for process A, which will increase its capacity to 550 units per week. This will cost $1m.
(2) Replace the machine in process B with an upgraded machine, costing $1.5m. This will double the capacity of process B.
(3) Buy an additional machine for process C, costing $2m. This will increase capacity in C by 300 units per week.

SOLUTION:

Financial viability

Buy C

Additional Sales = 50

$000

Benefit = 50 × $25,000

1,250

Cost

2,000

–––––

Net cost

750

Buy C and B

Additional sales from current position = 150

$000

Benefit = 150 × $25,000

3,750

Cost ($2m + $1.5m)

3,500

–––––

Net benefit

250

Buy C, B and A

Additional sales from current position = 250

$000

Benefit = 250 × $25,000

6,250

Cost ($2m +$1.5m +$1m)

4,500

–––––

Net benefit

1,750

The company will benefit by $1,750,000 by investing in all three machines.