Question

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?

Answer 1

\[a x^2+b x+c=\text{cost} \]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