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Math Help - Find total sales and individual sales

  1. #1
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    Find total sales and individual sales

    Ok I have this problem for HW and I have no idea how to solve it

    A small business sells two products: products S and product T. The selling cost of product S is $60 and costs $54 to sell; the business makes 60% profit for each sale of this product. The selling cost of product T is $70 and costs $56 to sell the business makes 40% profit for sale of this product. The overall fixed cost of the business is $202400. How many of each product do you have to sell and how many total sales do you have to make to break even.

    the furthest I got is the business makes $5.60 for sale of product T and 3.60 for sale of product S after that I don't know what to do
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  2. #2
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    I feel there is some missing info in the question. Normally, to find breakeven quantity, you'd divide the total fixed costs by profit per item (you need to cover your fixed costs to breakeven). Here, we have two products, and we don't know ratio between their sales, or their demand. Do we assume everything we market sells?

    If I want to cover fixed costs quickest, I'd sell T (highest profit margin per unit), ie quantity of T=$202,400/5.6=36,143 units or thereabouts.
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  3. #3
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    That's all the info I was given, someone from class told me I'm suppose to combine the products S and T numbers and end up with an equation like this
    9.2X - 202,400 = total sales. But it just doesn't make sense to me to combine two different variables also I wouldn't know where to go from there to see individual product sales.
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  4. #4
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    Quote Originally Posted by agonz024 View Post
    That's all the info I was given, someone from class told me I'm suppose to combine the products S and T numbers and end up with an equation like this
    9.2X - 202,400 = total sales. But it just doesn't make sense to me to combine two different variables also I wouldn't know where to go from there to see individual product sales.
    I, too, disagree with this proposal since we are clearly asked "How many of each product do you have to sell" and not just the total. In any case, combining their margins does not makes sense and the analysis is never done this way in real life.

    Perhaps you are expected to show the equation only? eg if X is S quantity of sales and Y is T's quantity, then we need to sell 3.6X+5.6Y=202400 to breakeven. I am sorry but I cannot see any way to find X or Y separately from the information given.
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  5. #5
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    i notice that 60% + 40% = 100%. does the question have a typo?

    Perhaps it was (change in red):

    A small business sells two products: products S and product T. The selling cost of product S is $60 and costs $54 to sell; the business makes 60% of total profit for each sale of this product. The selling cost of product T is $70 and costs $56 to sell the business makes 40% of total profit for sale of this product. The overall fixed cost of the business is $202400. How many of each product do you have to sell and how many total sales do you have to make to break even.
    In which case it is likely that there will be a unique break-even combination of S and T.
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  6. #6
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    Could be!
    In that case, the unit profits are $6 and $14 and the system of linear equations is: 6x+14y=202400, 6x/14y=60/40 which is solvable for x and y with nice round numbers for x and y)))
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