document.write( "Question 888529: Not sure if this will be too much but I need assistance with this problem.\r
\n" ); document.write( "\n" ); document.write( "What to do? (Hint: 200 x D is the same as 200D)\r
\n" ); document.write( "\n" ); document.write( "1. Option 1 - buy the part for 300 dollars per part.
\n" ); document.write( "2. Option 2 - purchase a machine that requires one operator (machine costs: 100,000 dollars and variable costs are 85 dollars per widget).
\n" ); document.write( "3. Option 3 - purchase a \"no human needed machine\" (machine costs: 250,000 dollars and variable costs are 30 dollars per widget).\r
\n" ); document.write( "\n" ); document.write( "Now then, find the breakeven point for \"demand\" (D) between options 1 and 2; 2 and 3. (Not you are not/not to find the breakeven point for \"demand for 1 and 3).\r
\n" ); document.write( "\n" ); document.write( "Find the breakeven point like this:\r
\n" ); document.write( "\n" ); document.write( "a. For 1/2
\n" ); document.write( "Cost per part (times (I'll use the symbol * to represent times) (D) = Fixed costs + Variable Cost per part * (D)
\n" ); document.write( "Remember, you're solving for \"D\"\r
\n" ); document.write( "\n" ); document.write( "b. For 2/3
\n" ); document.write( "Fixed costs + Variable Cost per part * (D) (for option 2) = Fixed costs + Variable Cost per part * (D)
\n" ); document.write( "Remember, you're solving for \"D\"\r
\n" ); document.write( "\n" ); document.write( "c. If demand is 1,500 widgets, which option is best?
\n" ); document.write( "d. If demand is 3,000 widgets, which option is best?
\n" ); document.write( "e. If demand is 300 widgets, which option is best?
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Algebra.Com's Answer #537511 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
let x equal the number of widgets.\r
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\n" ); document.write( "\n" ); document.write( "option 1 cost = 300 * x\r
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\n" ); document.write( "\n" ); document.write( "option 2 cost = 100,000 + 85 * x\r
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\n" ); document.write( "\n" ); document.write( "breakeven point is when these costs are equal to each other.\r
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\n" ); document.write( "\n" ); document.write( "300 * x = 100,000 + 85 * x\r
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\n" ); document.write( "\n" ); document.write( "solve for x to get x = 465.1162791...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 1 becomes 300 * 465.1162791... = 139,534.8837...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 2 becomes 100,000 + 85 * 465.1162791 = 139,534.8837...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 1 and option 2 is equivalent when the number of widgets is equal to 465.1162791...\r
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\n" ); document.write( "\n" ); document.write( "option 2 cost is 100,000 + 85 * x\r
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\n" ); document.write( "\n" ); document.write( "option 3 cost is 250,000 + 30 * x\r
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\n" ); document.write( "\n" ); document.write( "these 2 options break even when the cost for option 2 is the same as the cost for option 3.\r
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\n" ); document.write( "\n" ); document.write( "set these costs equal to each other and solve for x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "100,000 + 85 * x = 250,000 + 30 * x\r
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\n" ); document.write( "\n" ); document.write( "solve for x to get x = 2727.2727...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 2 becomes 100,000 + 85 * 2727.2727... = 331,818.1818...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 3 becomes 250,000 + 30 * 2727.2727... = 331,818.1818...\r
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\n" ); document.write( "\n" ); document.write( "cost for option 2 and 3 are equivalent when the number of widgets is equal to 2727.2727...\r
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\n" ); document.write( "\n" ); document.write( "if demand is 1500 widgets, these are the costs:\r
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\n" ); document.write( "\n" ); document.write( "option 1 = 300 * 1500 = 450,000
\n" ); document.write( "option 2 = 100,000 + 85 * 1500 = 227,500
\n" ); document.write( "option 3 = 250,000 + 30 * 1500 = 295,000\r
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\n" ); document.write( "\n" ); document.write( "the least cost option at 1500 widgets is option 2.\r
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\n" ); document.write( "\n" ); document.write( "if the demand is 3000 widgets, these are the costs:\r
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\n" ); document.write( "\n" ); document.write( "option 1 = 300 * 3000 = 900,000
\n" ); document.write( "option 2 = 100,000 + 85 * 3000 = 355,000
\n" ); document.write( "option 3 = 250,000 + 30 * 3000 = 340,000\r
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\n" ); document.write( "\n" ); document.write( "the least cost option at 3000 widgets is option 3.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if the demand is 300 widgets, these are the costs:\r
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\n" ); document.write( "\n" ); document.write( "option 1 = 300 * 300 = 90,000
\n" ); document.write( "option 2 and option 3 are both greater than 100,000 because of their fixed costs.\r
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\n" ); document.write( "\n" ); document.write( "the least cost option at 300 widgets is option 1.\r
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