To determine which company has a lower minimum cost, we need to compare the minimum values of the cost functions f(x) and g(x).
First, let's find the minimum value of f(x) by completing the square on the quadratic function f(x) = 0.05x^2 - 7x + 300.
f(x) = 0.05x^2 - 7x + 300
f(x) = 0.05(x^2 - 140x) + 300
f(x) = 0.05(x^2 - 140x + 4900 - 4900) + 300
f(x) = 0.05((x-70)^2 - 4900) + 300
f(x) = 0.05(x-70)^2 - 245 + 300
f(x) = 0.05(x-70)^2 + 55
Since the coefficient of the x^2 term is positive, the parabola opens upwards, so the vertex of the parabola represents the minimum value. The x-coordinate of the vertex is at x = 70.
Now let's find the minimum value by substituting x = 70 into the function:
f(70) = 0.05(70)^2 + 55
f(70) = 0.05(4900) + 55
f(70) = 245 + 55
f(70) = 300
So, the minimum cost for company 1 is $300.
Now let's compare this with the minimum values of the cost function g(x) for company 2:
The minimum value of g(x) is 899.50 when x = 1.
Therefore, company 1 has a lower minimum cost and the minimum value is $300.
he 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, determine which company has a lower minimum and find the minimum value.
1 answer
1 answer