the planning department of abstract office supplies has been asked to determine whether the company should…

the planning department of abstract office supplies has been asked to determine whether the company should introduce a new computer desk next year. the department estimates that $9000 of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be $300. the department also estimates that the revenue from each desk will be $750.\na. determine the revenue function r(x) from the sale of x desks. r(x)=750x\nb. determine the cost function c(x) for manufacturing x desks. c(x)=9000 + 300x\nc. find the number of desks that must be sold for the company to break even.

the planning department of abstract office supplies has been asked to determine whether the company should introduce a new computer desk next year. the department estimates that $9000 of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be $300. the department also estimates that the revenue from each desk will be $750.\na. determine the revenue function r(x) from the sale of x desks. r(x)=750x\nb. determine the cost function c(x) for manufacturing x desks. c(x)=9000 + 300x\nc. find the number of desks that must be sold for the company to break even.

Answer

Explanation:

Step1: Recall break - even condition

At break - even, revenue equals cost, i.e., $R(x)=C(x)$.

Step2: Set up the equation

We have $R(x) = 750x$ and $C(x)=9000 + 300x$. So, $750x=9000 + 300x$.

Step3: Solve for x

Subtract $300x$ from both sides: $750x-300x=9000$, which simplifies to $450x = 9000$. Then, divide both sides by 450: $x=\frac{9000}{450}=20$.

Answer:

20