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 $10,000 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 $800.\na. determine the revenue function r(x) from the sale of x desks. r(x)= \nb. determine the cost function c(x) for manufacturing x desks. c(x)= \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 $10,000 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 $800.\na. determine the revenue function r(x) from the sale of x desks. r(x)= \nb. determine the cost function c(x) for manufacturing x desks. c(x)= \nc. find the number of desks that must be sold for the company to break even.

Answer

Explanation:

Step1: Define revenue function

Revenue per desk is $800. So for $x$ desks, $R(x)=800x$.

Step2: Define cost function

Fixed cost of equipment is $10000$ and variable cost per - desk is $300$. So $C(x)=10000 + 300x$.

Step3: Find break - even point

Set $R(x)=C(x)$. So $800x=10000 + 300x$. Subtract $300x$ from both sides: $800x-300x=10000$, which simplifies to $500x = 10000$. Then $x=\frac{10000}{500}=20$.

Answer:

a. $R(x)=800x$ b. $C(x)=10000 + 300x$ c. $20$