Write an AMPL model file and a data file for the LP formulation for Problem below .Solve the LP in AMPL, and recordthe optimal solution and the optimal objective function value. Then modify the original filesto solve the modification given in part (b)-(i) Submit model and data files, as well as theoutput from the AMPL run.
A company produces two kinds of products. A product of the first type requires 1/4 hours of assembly labor, 1/8 hours of testing, and $1.2 worth of raw materials. A product of the second type requires 1/3 hours of assembly, 1/3 hours of testing, and S0.9 worth of raw materials. Given the current personnel of the company, there can be at most 90 hours of assembly labor and 80 hours of testing each day. Products of the first and second type have a market value of S9 and S8 respectively.
(a) Formulate a linear program that maximizes the daily profit of the company
(b) Consider the two modifications of the orifginal problem:
(i) Suppose that up to 50 hours of overtime assembly labor can be scheduled, at a cost of $7 per hour.
(ii) Suppose that the raw material supplier provides a 10% discount if the daily bill is above 300$.
Which of the above two elements two elements can be easily incorporated into a linear program formulation and how.