A company manufactures two kinds of calculators: Alpha and Beta. The company has got an order for manufacturing at least $2,500$ calculators in all. Both types of calculators are manufactured on the same machine and the total machine time available is $600$ machine hours. Each Alpha calculator takes $9$ minutes to manufacture while a Beta calculator requires $6$ minutes. The profit per piece on Alpha calculator is $100,$ and on Beta calculator is $50.$ Formulate the given problem as an LPP and solve using the Simplex method.