Problema Solution
Company ABC produces widgets. They have found that the cost, c (x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $23 to produce 2 widgets, $55 to produce 4 widgets, and $247 to produce 10 widgets. What is the total cost of producing 8 widgets?
Answer provided by our tutors
c(2) = 23
c(4) = 55
c(10) = 247
c(x) = a (x^2) + b(x) + c
Plugging in the points,
EQ1 23 = 4a + 2b + c
EQ2 55 = 16a + 4b + c
EQ3 247 = 100a + 10b + c
Now that you have three equations and three unknowns, its fairly simple to find the terms a, b and c.
From EQ1
EQ1i a = (23 - 2b - c) / 4
Plug that into EQ2
55 = 16[(23-2B-C)/4] + 4b + c
55 = 92 - 8b - 4c + 4b + c
4b + 3c = 37
EQ2i b = (37 - 3c) / 4
*I'm not a fan of giving away the entire answer, as I'm pretty sure you are not doing this as a recreational activity, and it's probably your homework, so this should serve as a "how to";
Combining EQ1i, EQ2i & EQ3 should yield values for a, b & c.
Putting those values into the quadratic equation, gives you the relationship of cost to widget production.
Plug in 8 as x, and you should get the cost.