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]
Accepted Solution
A:
The minimum production cost for company 2 is greater.
The minimum production cost for company 2 is at point 1, and it's 899.5.
Just looking at the function for company 1, we can infer that the minimum will be much lower. As x increases, costs will initially decrease (-7x will dominate 0.05x^2). Since 300 is the y intercept, it will be lower than 300 for some portion of the domain until it hits a minimum.