I can't seem to figure this quadratic -
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x
engines are made, then the unit cost is given by the function
C(x) = 0.2x^2 - 48x + 21,748
What is the minimum unit cost?
Do not round your answer.
Please help
When x= 120
y =18868. ( That is the minimum point in this quadratic, aka vertex.)
To find the minimum unit cost, we need to determine the vertex of the quadratic function. The vertex is the point where the function reaches its minimum value.
We can use the formula for the x-coordinate of the vertex, which is -b/2a, where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
In this case, the quadratic equation is 0.2x^2 - 48x + 21,748, so a = 0.2, b = -48, and c = 21,748.
Using the formula, we can calculate the x-coordinate of the vertex:
x-coordinate = -b/2a = -(-48)/(2 * 0.2) = 48/0.4 = 120
Now we substitute this x-coordinate back into the original equation to find the minimum unit cost:
C(x) = 0.2x^2 - 48x + 21,748
C(120) = 0.2 * 120^2 - 48 * 120 + 21,748
C(120) = 0.2 * 14,400 - 5,760 + 21,748
C(120) = 2,880 - 5,760 + 21,748
C(120) = 19,868
Therefore, the minimum unit cost is $19,868.