1. **Find the power set of A = [a,b,c,d]** The power set of a set is the set of all possible subsets, including the empty set and the set itself. Since A has 4 elements, the power set will have $2^4 = 16$ subsets. The subsets are: - $\emptyset$ - $\{a\}$ - $\{b\}$ - $\{c\}$ - $\{d\}$ - $\{a,b\}$ - $\{a,c\}$ - $\{a,d\}$ - $\{b,c\}$ - $\{b,d\}$ - $\{c,d\}$ - $\{a,b,c\}$ - $\{a,b,d\}$ - $\{a,c,d\}$ - $\{b,c,d\}$ - $\{a,b,c,d\}$ 2. **Find the break-even point for the revenue function $R = 25x - 100$** The break-even point occurs when revenue $R = 0$. Set the equation equal to zero: $$25x - 100 = 0$$ Add 100 to both sides: $$25x = 100$$ Divide both sides by 25: $$x = \frac{100}{25} = 4$$ So, the break-even point is when 4 units are sold. **Final answers:** - Power set of $A$ has 16 subsets as listed above. - Break-even point is at $x = 4$ units sold.