How many tote bags must the company sell each day to equal its daily cost for overhead,labor, and materials

Question

A company manufactures tote bags.The company spends $1200 each day for overhead expenses plus $9 per tote bag for labor and materials. The tote bags sell for $25 each. 

Answer 1

We can use the formula for profit, which states that profit = revenue - cost

 

Let's rewrite this as P(x) = R(x) - C(x)

 

Essentially, this problem wants to know when the company will break even, or when the profit equals zero. 

 

Let x = the number of tote bags sold

 

Our equation becomes

 

0 = 25x - [1200 + 9x]

 

0 = 25x - 1200 - 9x

 

16x - 1200 = 0

 

16x = 1200

 

x = 75

 

The company must sell 75 bags each day to break even

Answer 2

The expenses each day can be written as the equation E =9x + 1200 or in negative terms E = -9x - 1200

E=expenses, x= tote bags

 

The profit each day can be written as the equation P=25x

P=profit, x=tote bags

 

So to find the break even point, set the two equations equal to each other and solve

9x+1200 = 25x

subtract 9x from both sides to get

1200 = 16x

divide both sides by 16 and

75 = x

 

so if they sell 75 totes each day, the expenses would be 9(75) +1200 = $1,875 spent, and the profits would be 25(75) = $1,875 earned. 

 

So the company must sell 75 totes to equal it's daily expenses.