document.write( "Question 1168304: (a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from
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Algebra.Com's Answer #851637 by mccravyedwin(407) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "A student posted this problem back in September, 2020. I'll bet they'll get a\r\n" );
document.write( "big laugh when they are notified that 4 1/2 years later, they finally got an\r\n" );
document.write( "answer, now that they're no longer in school. \r\n" );
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document.write( "Notice the date:  168304 (2020-10-26 21:49:28)\r\n" );
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document.write( "The date disappears when we answer. \r\n" );
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document.write( "(a) A company has determined that its profit \r\n" );
document.write( "for a product can be described by a linear function. \r\n" );
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document.write( "Let the function be\r\n" );
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document.write( "y = mx + b, where y is profit, and x is the number of units.\r\n" );
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document.write( "The profit from the production and sale of 150 units is $455, \r\n" );
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document.write( "When x = 150, y = 455.  We substitute in y = mx+b.\r\n" );
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document.write( "455 = m(150) + b or\r\n" );
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document.write( "150m + b = 455.\r\n" );
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document.write( "and the profit from 250 units is $895.\r\n" );
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document.write( "When x = 250, y = 895.  We substitute in y = mx+b.\r\n" );
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document.write( "895 = m(250) + b or\r\n" );
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document.write( "250m + b = 895.\r\n" );
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document.write( "Solve the system of equations:\r\n" );
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document.write( "Subtract the two equations term by term and the b's cancel.\r\n" );
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document.write( "So the equation is \r\n" );
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document.write( "(i) What is the average rate of change of\r\n" );
document.write( "the profit for this product when between 150 and 250 units\r\n" );
document.write( "are sold?\r\n" );
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document.write( "That is the slope or 4.4 more dollars per unit sold.\r\n" );
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document.write( "(ii) Write the equation of the profit function\r\n" );
document.write( "for this product.\r\n" );
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document.write( " although you can write using P for y and U for x.\r\n" );
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document.write( "(iii) How many units give break-even \r\n" );
document.write( "for this product?\r\n" );
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document.write( "That's when the profit is 0\r\n" );
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document.write( "about 47.6 units give break-even for this product.\r\n" );
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document.write( "Sorry it took so 4.5 years to get an answer, but back then there were too\r\n" );
document.write( "many problems posted and not enough tutors.  Nowadays there are more tutors\r\n" );
document.write( "than posts.\r\n" );
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document.write( "Edwin

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