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
Y = 16, -16
explanation: the absolute value bars make the expression inside positive, if they were negative to begin with. so, a negative number like -16 becomes 16, and a positive number like 16 still stays the same
Answer:
6400
Step-by-step explanation:
Given the profit function ;
P(c) = –20c2 + 320c + 5,120
The maximum value is given by :
f(h) ; where, h = - b /2a
From P(C) ; a = - 20 ; b = 320
h = - b / 2a = - 320 / 2(-20) = - 320 / 40 = 8
c = h
P(8) = –20(8)² + 320(8) + 5,120
P(8) = - 1280 + 2560 + 5120
= 6400
2 is one, i really don’t remember this. I think 6 and 4 3 i think.
