Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of C = 400 – 5x + 0.125x2, where x is the number of gas grills produced. How many units should be produced each day to yield a minimum cost? I NEED HELP PLEASSEEEEEEEEE

The function given is a quadratic function, so the graph will be a parabola. It'll look similar to the photo attached. The minimum cost will be at the vertex of the parabola because that is its lowest point! To find the x-value of the vertex (which is what the question is looking for), use the vertex formula: x = -b/2a. The variable b is the coefficient of the x term in the function, and the variable a is the coefficient of the x² term. In this case, a = 0.125 and b = -5.
x = -(-5)/2(0.125)
x = 5/0.25
x = 20
So, 20 gas grills should be produced each day to maintain minimum costs. Hope that helps! :)

tardymanchester tardymanchester · Answer 2 · 2019-02-25T07:01:48+01:00

Answer:

20 units

Step-by-step explanation:

Given : Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of [tex]C = 400- 5x + 0.125 x^2[/tex], where x is the number of gas grills produced.

To find : How many units should be produced each day to yield a minimum cost?

Solution :

We observe that the given equation is in the form of quadratic equation

[tex]y=a x^2+bx+c[/tex]

The minimum or maximum value of a quadratic equation occurs at its vertex.

So, we have to find the vertex of the given equation,

[tex]x=-\frac{b}{2a}[/tex]

Given equation - [tex]C = 0.125 x^2-5x+400[/tex]

where, a=0.125 , b=-5, c=400

[tex]x=-\frac{-5}{2(0.125)}[/tex]

[tex]x=\frac{5000}{250}[/tex]

[tex]x=20[/tex]

The point at which value is minimize is x=20

To find the minimum cost put x=20 in the given equation,

[tex]C = 0.125 x^2-5x+400[/tex]

[tex]C = 0.125 (20)^2-5(20)+400[/tex]

[tex]C = 0.125 (400)-100+400[/tex]

[tex]C = 50+300[/tex]

[tex]C =350[/tex]

Therefore, 20 units should be produced each day to yield a minimum cost.