Question

A fast-food restaurant has a cost of production C(x)=12x+114 and a revenue function R(x)=6x. When does the company start to turn a profit?

Answer 1

Step-by-step explanation:

Given data

C(x)=12x+114

R(x)=6x.

The company will start to run on profit just when revenue equals the production cost, that is

C(x)=R(x)

equating the two expressions we have

12x+114=6x

solving for x we have

12x-6x+114=0

6x+114=0

6x=-114

x=-114/6

x=-19

Hence the company will start to run on proft when they start to produce above 19 items

Answer 2

Profit is the difference between the revenue and cost functions

A production greater than 19 will turn a profit

From the question, we have:

$\mathbf{R(x) = 6x}$

$\mathbf{C(x) = 12x + 114}$

So, the profit function is:

$\mathbf{P(x) = R(x) - C(x)}$

Substitute known values

$\mathbf{P(x) = 6x - 12x - 114}$

$\mathbf{P(x) = - 6x - 114}$

Equate to 0

$\mathbf{- 6x - 114 = 0}$

Collect like terms

$\mathbf{- 6x= 114}$

Divide both sides by -6

$\mathbf{x= -19}$

The above equation means that: A production greater than 19 will turn a profit

Read more about profit functions at:

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