Question

Suppose a widget manufacturer has:the total cost function C(x) = 25x + 5430 and the total revenuefunction: R(x) = 40xThe number of widgets the manufacturer has to sell to break even is:

Answer 1

362

Step-by-step explanation:

Given the cost function, C(x), and total revenue, R(x), as;

`\begin{gathered} C(x)=25x+5430 \\ R(x)=40x \end{gathered}`

Recall that the profit function, P(x), is given as;

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

Note that a break-even point is a point where the revenue starts overtaking the cost. At the break-even point, P(x) = 0, so we'll have;

`\begin{gathered} P(x)=0 \\ R(x)-C(x)=0 \\ 40x-(25x+5430)=0 \end{gathered}`

Let's clear the parentheses and solve for x;

`\begin{gathered} 40x-25x-5430=0 \\ 15x=5430 \\ x=(5430)/(15) \\ x=362 \end{gathered}`

We can see from the above that the number of widgets the manufacturer has to sell to break even is 362