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