Question

snappys, inc. is a company that produces digital cameras. they are planning to release a new line of cameras. snappys pays a fixed cost of $200,000 to introduce the new line, plus $100 per camera. they are planning to sell the cameras for $250 each. if $x$ denotes the number of individual cameras, what is minimum value of $x$ that should be sold so that the company makes a profit? note: in other words, how many cameras must be sold so that the sale of 1 more camera yields a profit? give your answer to the nearest integer. provide your answer below:

Explanation:

Step1: Set up cost and revenue functions

Cost function $C(x)=200000 + 100x$, Revenue function $R(x)=250x$.

Step2: Set up profit - making inequality

For profit, $R(x)>C(x)$. So $250x>200000 + 100x$.

Step3: Solve the inequality

Subtract $100x$ from both sides: $250x-100x>200000$, which simplifies to $150x>200000$. Then $x>\frac{200000}{150}=\frac{4000}{3}\approx1333.33$.

Step4: Round up to the nearest integer

Since $x$ represents the number of cameras and must be an integer, we round up $\frac{4000}{3}$ to 1334.

Answer:

1334