type the correct answer in each box. a music company is introducing a new line of acoustic guitars next…

type the correct answer in each box. a music company is introducing a new line of acoustic guitars next quarter. these are the cost and revenue functions, where x represents the number of guitars to be manufactured and sold: r(x)=120x c(x)=100x + 1840 the company needs to sell at least guitars for a total revenue of $ to start making a profit. reset next

type the correct answer in each box. a music company is introducing a new line of acoustic guitars next quarter. these are the cost and revenue functions, where x represents the number of guitars to be manufactured and sold: r(x)=120x c(x)=100x + 1840 the company needs to sell at least guitars for a total revenue of $ to start making a profit. reset next

Answer

Explanation:

Step1: Recall profit - making condition

Profit is made when $R(x)>C(x)$. So we set up the inequality $120x>100x + 1840$.

Step2: Solve the inequality

Subtract $100x$ from both sides: $120x-100x>100x + 1840-100x$, which simplifies to $20x>1840$.

Step3: Isolate x

Divide both sides of the inequality $20x>1840$ by 20: $x>\frac{1840}{20}=92$.

Step4: Find the revenue for break - even and profit

The revenue function is $R(x)=120x$. When $x = 92$, $R(92)=120\times92 = 11040$. To start making a profit, the company needs to sell at least 93 guitars. The revenue for 93 guitars is $R(93)=120\times93=11160$.

Answer:

93; 11160