Question

The following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x) = 0.05x2 − 7x + 300 The following table represents the production cost g(x), in dollars, for x number of units produced by company 2: x g(x) 0.6 899.58 0.8 899.52 1 899.50 1.2 899.52 1.4 899.58 Based on the given information, the minimum production cost for company _____ is greater. [Put 1 or 2 in the blank space]

Answer 1

1) production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.05x^2 − 7x + 300

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

x g(x)
0.6 899.58

0.8 899.52

1 899.50

1.2 899.52

1.4 899.58

3) Comparison: do a table for f(x) with the same x-values of the table for g(x).

x f(x) = 0.05x^2 − 7x + 300 g(x)

0.6 295.818 899.58

0.8 294.432 899.52

1 293.05 899.50

1.2 291.672 899.52

1.4 290.298 899.58

As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.

The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).

Answer: Based on the given information, the minimum production cost for company 2 is greater.