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
