63. minimum cost a manufacturer of lighting fixtures has daily production costs of c = 800 - 10x + 0.25x²…
63. minimum cost a manufacturer of lighting fixtures has daily production costs of c = 800 - 10x + 0.25x², where c is the total cost (in dollars) and x is the number of units produced. what daily production number yields a minimum cost?
Answer
Explanation:
Step1: Identify the function type
The cost function $C(x)=800 - 10x+0.25x^{2}$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.25$, $b=- 10$, $c = 800$.
Step2: Use the formula for the vertex of a quadratic function
For a quadratic function $y = ax^{2}+bx + c$, the $x$-coordinate of the vertex (which gives the value of $x$ for minimum or maximum) is $x=-\frac{b}{2a}$. Substitute $a = 0.25$ and $b=-10$ into the formula: $x=-\frac{-10}{2\times0.25}$
Step3: Calculate the value of x
First, simplify the denominator: $2\times0.25 = 0.5$. Then, $x=\frac{10}{0.5}=20$.
Answer:
20