Question

A person has a taco stand. He has found that his daily costs are approximated by Upper C left parenthesis x right parenthesis equals x squared minus 50 x plus 865​, where Upper C left parenthesis x right parenthesis is the​ cost, in​ dollars, to sell x units of tacos. Find the number of units of tacos he should sell to minimize his costs. What is the minimum​ cost?

Answer 1

Answer:

Therefore he should sell 25 units of tacos to minimize his cost .

The minimum cost is $240.

Step-by-step explanation:

Given function,

$C(x)= x^2-50x+865$

where C is the cost in dollar to sell x units of tacos.

We know that,

If a function y(x)= ax²+bx+c,

then the function is minimum at $x= -\frac{b}{2a}$

Here a= 1 , b= -50 and c= 865.

Therefore

$x= -\frac{(-50)}{2\times 1} =\frac{50}{2}=25$

Therefore he should sell  25 units of tacos to minimize his cost .

putting the value of x in the given function

C(25)=25²-(50×25)+865

        =240

The minimum cost is $240.