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Sandy's nails is looking at purchasing a new nail machine for her salon. The cost breakdown...

Sandy's nails is looking at purchasing a new nail machine for her salon. The cost breakdown for her current and potential systems are shown below

Current situation: $5000/year, variable Cost: $3/set

New Machine: Fixed Cost: $4000/year, Variable Cost: $5/pack

Currently, she is able to sell 2000 packs at $9 per pack.

How many unit sales will Sandy need to make in order to make more money with the new machinery?

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Answer #1

Current:

selling price = $9

variable cost = $3

contribution = selling price - variable cost

= 9 - 3

= 6

profit = contribution x sales - fixed costs

= 6 x 2000 - 5000

= 7000

New machine:

selling price = $9

variable cost = $5

contribution = selling price - variable cost

= 9 - 5

= 4

we want profit more than 7000

let x be the number of units sold

so 7000 = x*4 - 4000

x = 2750

sandy needs to sell more than 2750 units(i.e.,from 2751th unit onwards) in order to make more money with the new machinery

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