Suppose you need a piece of equipment for a project that has

Suppose you need a piece of equipment for a project that has a purchase price of $22,000. Assume it also had a daily operational cost of $750. Suppose you could lease the same piece of equipment for $1200 per day, including operational costs. Set up the equation that would determine when it makes sense financially to purchase instead of lease. Write out your formula and then explain when the purchase cost would equal the lease cost.

Solution

Let you are using the equipment for x days.

Total working cost if Purchased:

C(x)=22000+750x

Total working cost if leased:

C(x)=1200x

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Now find when the cost of both is same as

1200x=750x+22000

450x=22000

x 49

So If you use for 49 days both cost will be equal.