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i am having a tough time understanding the solutions in the technical article especially getting the calculations for the additional units sold.
Cat Co makes a product using three machines – X, Y and Z. The capacity of each machine is as follows:
x = 800 capacity per week
y -= 600 capacity per week
z = 500 capacity per weekThe demand for the product is 1,000 units per week. For every additional unit sold per week, net present value increases by $50,000. Cat Co is considering the following possible purchases (they are not mutually exclusive):
Purchase 1: Replace machine X with a newer model. This will increase capacity to 1,100 units per week and costs $6m.
Purchase 2: Invest in a second machine Y, increasing capacity by 550 units per week. The cost of this machine would be $6.8m.
Purchase 3: Upgrade machine Z at a cost of $7.5m, thereby increasing capacity to 1,050 units.
Required:
Which is Cat Co’s best course of action?Given that the product is made using all three machines, the most that can be made in a week is limited by the one with the lowest capacity.
At the moment that can only produce a maximum of 500 a week (because of Z).
So the only way they can produce (and therefore sell more) is to upgrade Z (purchase3). That would mean that Z had a capacity to produce 1,050, but they could not produce that many because the machine with the lowest capacity would be Y and so the most they could produce would be 600.
If they want to produce more than 600 then in addition to upgrading Z they would also have to buy a second machine Y (purchase 2) which would mean that Z would still have a capacity of 1,100 and Y would have a capacity of 1,150. However X would still only have a capacity of 800 and so the most they could produce per week would be 800.
The only way of being able to produce more than 800 would be to replace X (purchase 1) as well as Y and Z, because then they would be able to produce up to 1,100 per week (although obviously they would only choose to produce 1,000 because that is the maximum demand.)
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