The daily production costs C( in dollars per unit) for a manufacturer of lighting fixtures are given by the quadratic function C(X)=800-10X+0.25X2 where x is the number of units produced. How many fixtures should be produced to yield a minimum cost per unit
minimum cost is at the vertex of the parabola. As usual, that occurs at
x = -b/2a = 10/0.5
20
To find the number of fixtures that should be produced to yield a minimum cost per unit, we need to determine the value of x at the vertex of the quadratic function.
The quadratic function is given by C(x) = 800 - 10x + 0.25x^2. The vertex of a quadratic function is obtained when x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c.
In this case, a = 0.25, b = -10, and c = 800. Plugging these values into the vertex formula, we obtain:
x = -(-10) / (2 * 0.25)
x = 10 / 0.5
x = 20
Therefore, the minimum cost per unit will be obtained when 20 fixtures are produced.