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if the cost varies inversely as the number of notebooks, then when the number of notebooks goes up, the cost must go down.
\n" ); document.write( "cost of manufacturing 10,000 notebooks is $.5 * 10,000 = $5,000
\n" ); document.write( "how much will it cost when 18,000 notebooks are manufactured?
\n" ); document.write( "good question.
\n" ); document.write( "it will be less, but how much less will be determined by what the cost will be when 18,000 notebooks are manufactured.
\n" ); document.write( "if the cost is $.25, then the cost to manufacture 18,000 notebooks is 18,000*$.25 = $4500 which, in this example, winds up being less than the cost to manufacture 10,000 notebooks.
\n" ); document.write( "that's because i halved the cost but didn't double the number of notebooks.
\n" ); document.write( "the actual reduction in cost would be less.
\n" ); document.write( "for argument sake, say $.40 per notebook.
\n" ); document.write( "then the cost to manufacture 18,000 notebooks would be 18,000*$.4 = $7,200.
\n" ); document.write( "your equation shows 50/10,000 = x/18,000
\n" ); document.write( "it really should be 10,000*50 = x*18,000
\n" ); document.write( "that means that 10,000*50 cents each = 18,000 * x cents each
\n" ); document.write( "that equation gets you x = 10,000*50/18,000 = 27.7777777777777
\n" ); document.write( "that just means that if you sell 10,000 units at 50 cents, then in order to sell 18000 units at the same total price, you have to sell the 18,000 units at 27.7777777777 cents apiece.
\n" ); document.write( "10000*50 = 27.777777*18000
\n" ); document.write( "50,000 = 50,000
\n" ); document.write( "the cost per unit * the number of units equation has to be preserved whether you are selling 10,000 units or 18,000 units.
\n" ); document.write( "saying that the cost is inversely proportional means that as the number of units goes up, the cost per unit goes down.
\n" ); document.write( "what is missing is how much down.
\n" ); document.write( "you don't have enough information to determine that.
\n" ); document.write( "usually they will say for an increase of x units, the cost per unit will drop y cents.
\n" ); document.write( "example:
\n" ); document.write( "for an increase of 8000 units the cost per unit will drop 15 cents.
\n" ); document.write( "check the question again and see if there is something missing in the information you have for it.
\n" ); document.write( "they might also tell you there is a fixed cost and an incremental cost per unit.
\n" ); document.write( "a fixed cost is the same regardless of the number of units produced.
\n" ); document.write( "the incremental cost per unit is applied to each unit manufactured.
\n" ); document.write( "example:
\n" ); document.write( "fixed cost is $5,000 and the incremental cost per unit is 50 cents.
\n" ); document.write( "manufacturing 10,000 units costs $5,000 fixed cost + ($.5*10000) = $5,000 incremental cost. total cost is $10,000 / 10,000 units = $1.00 a unit
\n" ); document.write( "take the same fixed cost and same incremental cost but manufacture 20,000 units.
\n" ); document.write( "cost is now $5,000 fixed cost plus ($.5*20000) = $10,000 incremental cost.
\n" ); document.write( "total cost is $15,000 / 20,000 units = $.75 a unit.
\n" ); document.write( "fixed cost remained the same and incremental cost per unit remained the same.
\n" ); document.write( "total cost went up, but the total cost per unit went down because the same fixed cost is being divided among 20,000 units rather than 10,000. \n" ); document.write( "