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