Question

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 bsp $ 16 comma 000 $16,000 of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be $ 250.$250. The department also estimates that the revenue from each desk will be $ 650.$650.

a. Determine the revenue function​ R(x) from the sale of x desks. ​R(x)equals=nothing
b. Determine the cost function​ C(x) for manufacturing x desks. ​C(x)equals=nothing
c. Find the number of desks that must be sold for the company to break even. nothing

Answer 1

a) R(x)=650x

b)C(x)=16000+250x

c)the number of desks that must be sold for the company to break even is 40

Explanation:

Cost of manufacturing equipment = $16000

Let the no. of desks be x

Cost of constructing 1 desk = $250

Cost of constructing x desks = 250x

Total cost = 16000+250x

Let C(x) denotes the cost function of x desks

So, C(x)=16000+250x

Revenue from 1 desk = $650

Revenue from x desks = $650x

Let the revenue function​ be R(x) for x desks

So, R(x)=650x

a) R(x)=650x

b)C(x)=16000+250x

c) Find the number of desks that must be sold for the company to break even.

So, C(x)=R(x)

`16000+250x=650x`

`16000=400x`

`40=x`

c)So, the number of desks that must be sold for the company to break even is 40