A cruise ship is planning its menu for the next trip. Vacationers like eating steak, lobster, and chicken. The chef of the cruise ship has decided to plan for at least half of all booked passengers to have a steak dinner, for at least a quarter of all passengers to have lobster, and the rest to have chicken. Steak dinners cost the cruise company $8, lobsters cost $15, and chicken costs the line $4. On the next cruise, there are 400 passengers booked. In addition, the cruise line told the chef to plan for an additional 25% more meals than bookings. Help the chef determine the optimum mix of meals to minimize their food costs. Determine the optimal solution and let the chef know how much it will cost to prepare this mix.