Answer:
Manufacture more than 24 items to make a profit.
Step-by-step explanation:
Let's find the Revenue function:
Revenue ([tex]R[/tex]) = Price per pair * Number of pairs sold
[tex]R(x)=130x[/tex]
Now let's find the profit function:
Profit ([tex]P(x)[/tex]) = Revenue ([tex]R(x)[/tex]) - Cost [tex]C(x)[/tex]
([tex]P(x)[/tex]) = ([tex]R(x)[/tex]) – [tex]C(x)[/tex]
[tex]P(x)=130x-(2950+6x+0.1x^{2} )[/tex], Where, ([tex]0\leq x\leq 500[/tex])
The requirement to make a profit:
[tex]P(x)\geq 0[/tex]
⇒[tex]130x-(2950+6x+0.1x^{2} )\geq 0[/tex]
[tex]x=24.265[/tex] or x=1215.735
Therefore, they should manufacture more than 24 items to make a profit.
