Write the following inequality in slope-intercept form. 6x + 2y ≤ –46

a. y ≤ –3x + 23

b. y ≤ –3x – 23

c. y ≥ –3x – 23

d. y ≥ –3x + 23

6x + 2y ≤ –46
2y ≤  -6x - 46
  y ≤  -3x - 23

answer is B. y ≤ –3x – 23

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).

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