algebra 2 question

Question

the function for the cost of materials to make a hat is f(x)=1/2x+1, where x is the number of hats. The function for the selling price of those hats is g(f(x)), where g(x)=x+2. Find the selling price of 10 hats

Answer 1

g(f(x)) = f(x)+2 = 1/2x+1+2 = selling price per hat

g(f(10)) = 1/2(10)+1+2 = 1/20+1+2 = $3.05

Cost per hat, with 10 hats is $1.05, 1/20+1. Profit is always $2 per hat or total profit of $20 on 10 hats

10 hats cost $10.50. Total sales if all 10 sold is $30.50 Total profit $30.50-$10.50=$20

Always a per hat markup of $2

There's a volume decrease in per hat cost. Just one hat costs 1/2+1 = $1.50

But with 10 hats the per hat cost decreases to $1.05