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A high school purchases a printing machine that can put lettering on clothing for $6,000. The school plans to print T-shirts with the school logo and sell them. Each T-shirt costs the school $4 and will sell for $12. How many T-shirts must the school sell before breaking even?

User Dave Morse
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2 Answers

1 vote
The answer is 175 so u just divide
User Allan F
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4 votes

Let's assume

number of T-shirts is x

Firstly , we will find cost function

Calculation of cost function:

A high school purchases a printing machine that can put lettering on clothing for $6,000

so, cost of printing machine =$6000

initial cost =6000

Each T-shirt costs the school $4

so, total cost =6000+4*x


C(x)=6000+4x

Calculation of selling price function:

we are given

Each T-shirt costs the school will sell for $12

so,

total selling price =12x


S(x)=12x

Break-even point:

In break-even point , selling price = cost price

so,


S(x)=C(x)

now, we can plug value


12x=6000+4x

now, we can solve for x


12x-4x=6000


8x=6000


x=750

So, the number of T-shirts are 750.........Answer

User Tayeb
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