Charlotte is knitting hats and scarves to sell on her online store. She has 20 balls of yarn and needs one-half a ball for each hat and a full ball for each scarf It takes her 5 hours to make one hat and 4 hours to make one scarf, and she can spend a maximum of 110 hours knitting this month. Charlotte makes a profit of $8 for every hat she sells and $6 for every scarf she sells.

The system of inequalities that represents this situation , {12x+y≤205x+4y≤110, is shown graphed in the first quadrant with the number of hats she makes along the x-axis and the number of scarves she makes along the y-axis. The equation that represents the total profit (P) that Charlotte earns from selling all her hats and scarves is P=8x+6y.

What combination of hats and scarves allows Charlotte to maximize her profit?

If Charlotte makes 40 hats and 0 scarves, she will have a maximum profit of $320.

If Charlotte makes 22 hats and 0 scarves, she will have a maximum profit of $176.

If Charlotte makes 10 hats and 15 scarves, she will have a maximum profit of $170.

If Charlotte makes 15 hats and 10 scarves, she will have a maximum profit of $180.

if Charlotte makes 0 hats and 20 scarves, she will have a maximum profit of $120.

If Charlotte makes 0 hats and 28 scarves, she will have a maximum profit of $168.