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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, the minimum production cost for company :blank:is greater.

[Put 1 or 2 in the blank space]

Verified Answer :

meerkat18

company 1: f(x) = 0.25x² - 8x + 600
f(6) = 0.25(6²) - 8(6) + 600 = 9 - 48 + 600 = 561
f(8) = 0.25(8²) - 8(8) + 600 = 16 - 64 + 600 = 552
f(10) = 0.25(10²) - 8(10) + 600 =  25 - 80 + 600 = 545
f(12) = 0.25(12²) - 8(12) + 600 = 36 - 96 + 600 = 540
f(14) = 0.25(14²) - 8(14) + 600 = 49 - 112 + 600 = 537

company 2: 
  x       g(x)
  6        862.2
  8        856.8
10        855
12        856.8
14        862.2

Based on the given information, the minimum production cost of company 2 is greater than the minimum production cost of company 1.

The minimum production cost of company 2 is greater than the minimum production cost of company 1.

How to find Production Cost?

Using the given input values, we have;

For Company 1, the respective production costs are;

f(x) = 0.25x² - 8x + 600

f(6) = 0.25(6²) - 8(6) + 600 = 561

f(8) = 0.25(8²) - 8(8) + 600 = 552

f(10) = 0.25(10²) - 8(10) + 600 = 545

f(12) = 0.25(12²) - 8(12) + 600 = 540

f(14) = 0.25(14²) - 8(14) + 600 = 537

For company 2, we are given the various production costs as;

x g(x)

6 862.2

8 856.8

10 855

12 856.8

14 862.2

From the above production cost values, we can deduce that the minimum production cost of company 2 is greater than the minimum production cost of company 1.

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