anonymous
  • anonymous
the company discovered that it costs $37 to produce 3 calculators, $213 to produce 7 calculators and $658 to produce 12 calculators. using the quadratic funtion, what is the total cost of producing 8 calculators?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[a x^2+b x+c=\text{cost} \]where x is the number of calculators produced. Plugging in the data point values for each of the cost/volume experience, yields three equations in three unknowns: {9 a + 3 b + c = 37, 49 a + 7 b + c = 213, 144 a + 12 b + c = 658} Solving the above for a, b and c and plugging in those values in the cost equation gives: \[5 x^2-6 x+10=\text{cost} \]At x = 8, the cost from the cost equation is 282

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