To make a package of all-beef hot dogs ( \(x\) ), a factory uses one pound of beef; to make their regular all-meat hot dogs ( \(y\) ), they use \(1 / 2\) pound of beef and \(1 / 2\) pound of pork. The profit on the package of all-beef hot dogs is \(\$ 2.40\) per pack; the profit on the all-meat hot dogs is \(\$ 3.20\) per pack. If there are 400 pounds of beef and 250 pounds of pork available, how many of each product should the factory make to maximize their profit?

Use the four steps for solving linear programming problems to solve.