Develop the Mathematical LP model for the following problem:

Two products are manufactured sequentially on two machines. The time available on each machine is 8 hours per day and may be increased by up to 4 hours of overtime, if necessary, at an additional cost of $110 per hour. The table below gives the production rate on the two machines as well as the price per unit of the two products. Develop an LP model to determine the optimum production schedule, and the recommended use of overtime, if any. Solve the problem using AMPL, Solver, or TORA.

\begin{tabular}{lcc} \hline & \multicolumn{2}{c}{ Production rate (units/hr) } \\ \cline { 2 - 3 } & Product 1 & Product 2 \\ \hline Machine 1 & 5 & 5 \\ Machine 2 & 8 & 4 \\ Price per unit (\$) & 120 & 128 \\ \hline \end{tabular}