Answer:
362
Explanation:
Given the cost function, C(x), and total revenue, R(x), as;
[tex]\begin{gathered} C(x)=25x+5430 \\ R(x)=40x \end{gathered}[/tex]
Recall that the profit function, P(x), is given as;
[tex]P(x)=R(x)-C(x)[/tex]
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;
[tex]\begin{gathered} P(x)=0 \\ R(x)-C(x)=0 \\ 40x-(25x+5430)=0 \end{gathered}[/tex]
Let's clear the parentheses and solve for x;
[tex]\begin{gathered} 40x-25x-5430=0 \\ 15x=5430 \\ x=\frac{5430}{15} \\ x=362 \end{gathered}[/tex]
We can see from the above that the number of widgets the manufacturer has to sell to break even is 362
