To make one package of all-beef hot dogs, a manufacturer uses 1 lb of beef; to make one package of regular hot dogs, the manufacturer uses 1/2 lb each of beef and pork. The profit on the all-beef hot dogs is 40 cents per pack, and the profit on regular hot dogs is 30 cents per pack. If there are 200 lb of beef and 150 lb of pork available, how many packs of all-beef and how many packs of regular hot dogs should the manufacturer make to maximize the profit? What is the profit?

Solve the linear programming problems.