Widget Wonders produces widgets. They

have found that the cost, o (x), of making x

widgets is a quadratic function in terms of x.

The company also discovered that it costs

$20.50 to produce 3 widgets. $60.50 to

produce 7 widgets, and $133 to produce 12

widgets.

What is the total cost of producing nine widgets

Find the total cost of producing 5 widgets. Widget Wonders 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 $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.

OK ... so we have

a (7) ^2 + b (7) + c = 23.50 → 49a + 7b + c = 23.50 (1)

a (3) ^2 + b (3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have

40a + 4b = 8 → 10a + b = 2 (2)

Also

a (12) ^2 + b (12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us

95a + 5b = 32.50

And using (2) we have

95a + 5b = 32.50 (3)

10a + b = 2.00 multiplying the second equation by - 5 and adding this to (3), we have

45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have

10 (1/2) + b = 2

5 + b = 2 b = - 3

And we can use 9a + 3b + c = 15.50 to find "c"

9 (1/2) + 3 (-3) + c = 15.50

9/2 - 9 + c = 15.50

-4.5 + c = 15.50

c = 20

So our function is

c (x) = (1/2) x^2 - (3) x + 20

And the cost to produce 5 widgets is = $17.50