Ichabod Poodleson owns a dog collar making business. He sells rhinestone studded

Question

Ichabod Poodleson owns a dog collar making business. He sells rhinestone studded dog collars that he hand makes. Ichabod spends dollar 4.75 on materials for each studded dog collar, Independent of any fixed costs. Last week Ichabod made 72 dog collars at a total cost of dollar 590. This total cost includes Ichabod's fixed costs (i.e. marketing, web hosting, etc.). Ichabod sells each dog collar for a price of dollar 12.50. Assuming that both cost and revenue are linear, how many dog collars must Ichabod produce and sell in a week order to break even? No rounding is needed.

Explanation / Answer

fixed cost =590-(72*4.75)

fixed cost =248$

let number of dog collars made =x

cost function =248 + 4.75x

revenue function =12.5x

for break even revenue =cost

12.5x=4.75x +248

x(12.5-4.75)=248

x=248/(12.5-4.75)

x=32

32 dog collars must be produced and sell ina week order to break even

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