(08.05 MC) The following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x) = 0.25x2 − 8x + 600 The following table represents the production cost g(x), in dollars, for x number of units produced by company 2: x g(x) 6 862.2 8 856.8 10 855 12 856.8 14 862.2 Based on the given information, determine which company has a lower minimum and find the minimum value. a g(x) at (10, 855) b f(x) at (16, 536) c g(x) at (16, 536) d f(x) at (10, 855)
(08.05 MC)
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.25x2 − 8x + 600
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
6 862.2
8 856.8
10 855
12 856.8
14 862.2
Based on the given information, determine which company has a lower minimum and find the minimum value.
a
g(x) at (10, 855)
b
f(x) at (16, 536)
c
g(x) at (16, 536)
d
f(x) at (10, 855)
ANSWER:
To determine which company has a lower minimum cost, we need to compare the minimum values of their cost functions.
For Company 1, the cost function is given as f(x) = 0.25x^2 - 8x + 600. To find the minimum value, we can use the vertex formula x = -b / (2a), where a = 0.25 and b = -8.
Using the formula, we find that the x-coordinate of the vertex is x = -(-8) / (2 * 0.25) = 16. Substituting this value into the equation, we can find the corresponding y-coordinate: f(16) = 0.25(16)^2 - 8(16) + 600 = 536.
For Company 2, the given table provides the cost values for different values of x. From the table, we see that the minimum cost occurs at x = 10, with a corresponding cost value of 855.
Comparing the minimum values, we see that the minimum cost for Company 1 is 536, and the minimum cost for Company 2 is 855. Since 536 is lower than 855, we can conclude that Company 1 has a lower minimum cost.
Therefore, the correct answer is:
b) f(x) at (16, 536)
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0 Response to "(08.05 MC) The following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x) = 0.25x2 − 8x + 600 The following table represents the production cost g(x), in dollars, for x number of units produced by company 2: x g(x) 6 862.2 8 856.8 10 855 12 856.8 14 862.2 Based on the given information, determine which company has a lower minimum and find the minimum value. a g(x) at (10, 855) b f(x) at (16, 536) c g(x) at (16, 536) d f(x) at (10, 855)"
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