question department stores are about to release a new makeup line, and a promotional kit will be sold for…

question department stores are about to release a new makeup line, and a promotional kit will be sold for $42.75. the cost to produce the kits can be determined by the cost function, where x is the number of kits to be produced and sold: c(x)=28.25x + 8,250. type the correct answer in the box. to the nearest whole number, the company must sell makeup kits before it starts to earn a profit. submit

question department stores are about to release a new makeup line, and a promotional kit will be sold for $42.75. the cost to produce the kits can be determined by the cost function, where x is the number of kits to be produced and sold: c(x)=28.25x + 8,250. type the correct answer in the box. to the nearest whole number, the company must sell makeup kits before it starts to earn a profit. submit

Answer

Explanation:

Step1: Set up profit - inequality

Profit $P(x)$ is revenue minus cost. Revenue $R(x)=42.75x$ and cost $C(x)=28.25x + 8250$. The company starts to earn a profit when $P(x)=R(x)-C(x)>0$. So, $42.75x-(28.25x + 8250)>0$.

Step2: Simplify the inequality

Expand the left - hand side: $42.75x-28.25x-8250>0$. Combine like terms: $(42.75 - 28.25)x-8250>0$, which gives $14.5x-8250>0$.

Step3: Solve for x

Add 8250 to both sides of the inequality: $14.5x>8250$. Then divide both sides by 14.5: $x>\frac{8250}{14.5}\approx568.97$.

Answer:

569