The cost, in dollars, for a doll company to produce x number of dolls is given by the function below.

1) Cost in dollars: d(x) = 0.1x^2 - 14x + 750

2) The minium cost corresponds to the vertex of the function

3) Rearrange the equation to the vertex form: d(x) = A(x - h)^2 + k, where the vertex is (h, k).

4) Rearrangment step by step:

Extract common factor 0.1 from the first two terms: 0.1 [ x^2 - 140x] + 750

Complete a perfect square:

0.1 [ (x - 70)^2 - 4900] + 750 = 0.1 (x - 70)^2 - 490 + 750 = 0.1(x - 70)^2 + 260

=> vertex = (70,260)

5) Conclusion the minium cost is $260 at x = 70

the minimum cost of production is $260 for 70 dolls.