word problem

Question

mitchell starts a business manufactoring bobbles heads sports fighures. His intial cost is 3300. each figure costs 450 to manufacture. each figure is sold for 1050. hom many figures must be manufactured and sold before he makes a profit.

Answer 1

Hello, Juan

 

Those are some expensive bubble heads  !!! Are you sure about the numbers? OK.  If you made a mistake just change them. 

 

Profit= Total Revenue- Total cost

Total Cost= Fixed Cost + Variable Cost

Total Cost= 3,300+ 450x                         450x Means that each bubble head cost $450 to produce

Total Revenue= 1050 x                            1050x means that he sell them a 1,050 each

 

Now that you need to find is the value of x where the Total Cost = Total revenues, or the break even point.  At this point you are neither making or loosing any money.  Below that point, you are loosing money, and above that point you are making a profit. 

 

TC=TR

3,300 + 450X= 1,050 x                        Subtract 450x from both sides

          -450x      -450x

3,300              =600x                           Divide both sides by 600          

    5.5              = x                              

Since you cannot sell 1/2 of a bubble head, we must use 6.  If he sell 6 or more, he will be making a profit. Lower than 6, he will be loosing money.  Make sure you check the numbers.

 

I hope this helps. 

 

D. Y. Taylor

Answer 2

costs:

 

let x be the number of figures sold before making a profit:

 

so,

 

-3300 - 450x + 1050x = 0

 

we set above equal to 0 to get the break even point.

 

3300 = 600x

 

x = 5.5

 

you can not sell a half so, we round off to next higher integer.

 

6 sales