Question

Superior Hammer has a fixed weekly cost of $120.00, and variable costs of $2.00 for making a hammer.

A. If x represents the number of hammers, in hundreds, manufactured each week, write a weekly cost function, C, for Superior hammer.

B. The function R(x)= -0.5x squared+ 18x describes the revenue Superior Hammer takes in each week, R(x), in thousands, from the sale of x hammers, in hundreds. Use this revenue function and your cost function from part a.) to write a profit function, P.

Really need help

Answer 1

Explanation:

Here,

fixed cost=120

variable cost for each hammer is 2

So, for x number of hammers,

variable cost=2x

So,

Total cost=2x+120

Hence, answer for (A) is

C(x)=2x+120

B)

`R(x)=-0.5x^(2) +18x`

we know,

Profit=Revenue-Cost

So, if P is the profit,

then profit function P(x) is,

`P(x)=R(x)-C(x)\\=-0.5x^(2) +18x-(2x+120)\\=-0.5x^(2) +18x-2x-120\\=-0.5x^(2) +16x-120`

So,

profit function is,

`P(x)=-0.5x^(2) +16x-120`