Because of economies of scale, the cost of production of the second gadget is half the first one which costs c dollars to produce. The production of the third gadget costs half of the second, etc. What is the value of c?
1. The sum of the costs of the third and fourth gadgets is $9.
2. The sum of the costs of the second and the ninth gadget is $${24}\cdot\frac{2^7+1}{2^8}$$ dollars.