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.

This law is sometimes called the grouping property. as you can see, regardless of how the numbers are grouped, the answer is still 13. the associative law of multiplication is similar to the same law for addition. it says that no matter how you group numbers you are multiplying together, you will get the same answer.