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. What is the total cost producing 5 widgets?

Theres not really any way to tell because the cost per widget is highest when making three, lowest when making 7, but then increases when making 12. If the cost didnt rise when making 12 and instead followed the trend of the more widgets you make, the cheaper it is per widget

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