Question

Suppose a company has fixed costs of $350 and variable cost of 0.49 x+1160 dollares per item. Suppose theselling price is -0.51 x+1340 dollars per unit.Find the cost function. C(x) =Find the revenue function. R(x) =Find the profit function. P(x) =

Answer 1

We will have that:

`C(x)=F+Vx`

Here F is the fixed cost, V is the variable cost per unit and x the number of units; so the cost function is:

`C(x)=350+(0.49x+1160)x\Rightarrow C(x)=0.49x^2+1160x+350`

Now, we remember that the Revenue function is given by:

`R(x)=px`

Here p is the price per item and x the number of items; so the revenue function is:

`R(x)=(-0.51x+1340)x\Rightarrow R(x)=-0.51x^2+1340x`

Finally, we remmeber that the profic function is given by:

`P(x)=R(x)-C(x)`

So, the profit function is given by:

`P(x)=(-0.51x^2+1340x)-(0.49x^2+1160x+350)`
`\Rightarrow P(x)=-x^2+180x-350`