Question

The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.15x2 − 6x + 400

The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:


x g(x)
50 75
60 60
70 55
80 60
90 75


Based on the given information, the minimum production cost for company _____ is greater.
[Put 1 or 2 in the blank space]

Answer 1

The answer is confirmed 1. Just took it.

Explanation:

Answer 2

Company 1 is greater.

Explanation:

Given,

The function that shows the production cost of company 1,

`f(x)=0.15x^2-6x+400`

Differentiating with respect to x,

We get,

`f'(x)=0.30x-6`

Again differentiating,

`f''(x)=0.30`

For minimum or maximum,

f'(x) = 0,

`\implies 0.3x-6=0`

`\implies x = 20`

Since, at x = 20, f''(x) = Positive,

So, f(x) is minimum at x = 20,

⇒ Minimum cost in company 1 is,

`f(20)=0.15(20)^2-6(20)+400`

`=340`

Also, by the given table,

The minimum cost of company 2 is at x = 70,

g(70) = 55,

Since, 340 > 55,

Hence, Based on the given information, the minimum production cost for company 1 is greater.