the cost of a computer system increases with increased processor speeds. the cost c of a system as a…

the cost of a computer system increases with increased processor speeds. the cost c of a system as a function of processor speed is estimated as c = 15s² - 8s + 1300, where s is the processor speed in mhz. find the processor speed for which cost is at a minimum. \na. 0.4 mhz\nb. 2.1 mhz\nc. 5.3 mhz\nd. 0.3 mhz

the cost of a computer system increases with increased processor speeds. the cost c of a system as a function of processor speed is estimated as c = 15s² - 8s + 1300, where s is the processor speed in mhz. find the processor speed for which cost is at a minimum. \na. 0.4 mhz\nb. 2.1 mhz\nc. 5.3 mhz\nd. 0.3 mhz

Answer

Explanation:

Step1: Identify the function type

The cost function $C(S)=15S^{2}-8S + 1300$ is a quadratic function of the form $y = ax^{2}+bx + c$, where $a = 15$, $b=-8$, $c = 1300$.

Step2: Use the formula for the vertex of a quadratic

For a quadratic function $y=ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the minimum for $a>0$) is $x=-\frac{b}{2a}$. Here, the processor speed $S$ for minimum cost is given by $S=-\frac{b}{2a}$. Substitute $a = 15$ and $b=-8$ into the formula: $S=-\frac{-8}{2\times15}=\frac{8}{30}\approx0.267\approx0.3$ MHz.

Answer:

D. 0.3 MHz