Question

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

Answer 1

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! :)

Answer 2

20 units

Explanation:

Given : Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of
`C = 400- 5x + 0.125 x^2`, 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

`y=a x^2+bx+c`

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

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

`x=-(b)/(2a)`

Given equation -
`C = 0.125 x^2-5x+400`

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

`x=-(-5)/(2(0.125))`

`x=(5000)/(250)`

`x=20`

The point at which value is minimize is x=20

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

`C = 0.125 x^2-5x+400`

`C = 0.125 (20)^2-5(20)+400`

`C = 0.125 (400)-100+400`

`C = 50+300`

`C =350`

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