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1 month ago

The daily production cost, C, for x units is modeled by the equation: C = 200 – 7x + 0.345x2

1 answer:

8 0

C(x) = 200 - 7x + 0.345x^2

The domain consists of all feasible x-values (i.e., units produced), including all positive integers and zero, if only whole units are deemed relevant.

The range includes all potential outcomes for c(x), or possible costs.

This can be derived by recognizing that c(x) is a parabolic function, which can be graphed to identify the vertex, roots, y-intercept, and its shape (which opens upward since the coefficient of x^2 is positive). Also, ensure costs remain positive.

You might substitute some values for x for clarity, for example:

x y
0 200
1 200 - 7 + 0.345 = 193.345
2 200 - 14 + 0.345 (4) = 187.38
3 200 - 21 + 0.345(9) = 182.105
4 200 - 28 + 0.345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42

10 200 - 70 + 0.345(100) = 164.5
11 200 - 77 + 0.345(121) = 164.745

The function lacks real roots, indicating costs will never fall to zero.

The function begins at c(x) = 200, declines until the vertex (x = 10, c = 164.5), and then starts to rise.

Thus, the range extends from 164.5 to infinity, limited to positive integer solutions for x.

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