The following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x) = 0.05
x2 − 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]
<span>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) = </span><span>0.05x^2 − 7x + 300 g(x)
</span><span><span>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 </span>
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.
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