Will it be p = 3? 2x+ 1 substitution simplification: y = 16? 4x+ 1？ X (0 ≤ x ≤ a)。 -(6 points)
(ⅱ)y′=？ 1? ? 4(x+ 1)2=？ (x+ 1)2+4(x+ 1)2=？ x2+2x？ 3(x+ 1)2=？ (x+3)(x？ 1)(x+ 1)2
When a≥ 1 and y' > 0, x ∈ (0, 1), then the function y = 16? x？ When 4x+ 1 monotonically increases x ∈ (1, a), y' < 0, then the function y = 16? x？ 4x+ 1 monotonically decreases at (1, a).
When the promotion cost is 6.5438+0 million yuan, the profit of the manufacturer is the largest; ——(9 points).
When a < 1, because the function y = 16? x？ 4x+ 1 monotonically increases on (0, 1) y = 16? x？ 4x+ 1 monotonically increases on [0, a],
Therefore, when x=a, the function has a maximum value, that is, when the promotion cost is one million yuan, the profit of the manufacturer is the largest.
To sum up, when a≥ 1, the promotion cost is 1 10,000 yuan, and the profit of the manufacturer is the largest;
When A < 1, the manufacturer's profit is the largest if he invests 1 ten thousand yuan in promotion expenses (12 points).
(Note: When a≥ 1, it can also be: y = 17? (4x+ 1+x+ 1)≤ 17？ 24x+ 1×(x+ 1)= 13，
If and only if 4x+ 1 = x+ 1, that is, x = 1, the above formula is equal)