The monthly cost in dollars from producing x units of an item is given by the cost function C(x)=2x^2-160x+18400. How many units will result in the minimum cost?
I do not know how to start this problem. Thank you for your help!
this just a parabola. You know that for
ax^2+bx+c, the vertex (minimum) is at x = -b/2a.
so, plug in your values of a and b to find the desired x.
89
To find the number of units that will result in the minimum cost, we need to determine the x-value (number of units) at which the cost function C(x) is at its minimum. Here is how you can solve this problem step by step:
Step 1: Understand the problem
The cost function is given as C(x) = 2x^2 - 160x + 18400, where x represents the number of units. The goal is to find the value of x that minimizes the cost C(x).
Step 2: Identify the minimum point
Since we want to find the minimum cost, we are interested in the minimum point of the cost function. The minimum point of a quadratic function is located at its vertex.
Step 3: Find the x-coordinate of the vertex
The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a). In our case, the cost function is C(x) = 2x^2 - 160x + 18400. Here, a = 2 and b = -160, so we can substitute these values into the formula to find the x-coordinate of the vertex.
x = -(-160) / (2 * 2)
x = 160 / 4
x = 40
So, the x-coordinate of the vertex is 40.
Step 4: Interpret the result
The x-coordinate of the vertex represents the number of units that will result in the minimum cost. Therefore, 40 units will result in the minimum cost.
So, the answer to the question is 40 units.