A local steakhouse is catering a party, and they are going to grill hot dogs and bratwurst. Their huge grill has 2304 square inches of grilling space. Each hot dog requires 24 square inches of grilling space, and the bratwurst requires 16 square inches of grilling space. The company that hired them gives them 8 hours (480 mins) to grill all of the food. Each hot dog takes 4 minutes to grill, and each bratwurst takes 8 minutes to grill. The steakhouse has 45 servings of their original seasoning for the bratwurst only. If they charge $4 for a hot dog and $6 for a bratwurst, how many of each should they sell to make the most money? Inequalities:
24h + 16b ≤ 2304 (grill space)
480 ≥ 4h + 8b (time)
45 ≥ b (sauce)
h ≥ 0 (hot dogs to make)
b ≥ 0 (bratwurst to make)

Money Equation: $4h + $6b = m

Graph the inequalities on the same plane. Find the intersection points and plug them into the money equation to answer the maximum profit.