Steel bars of length 11 meters arrive at a company from its supplier. The bars must be cut into smaller lengths to meet weekly demand and minimize wastage. For each bar the company must decide:
(i) Whether to cut it into two 5 metre lengths; or
(ii) Whether to cut it into one 2 metre length, one 3 metre length and one 5 metre length.
In the next week the company requires 105 bars that are 2 metres long, 153 bars that are 3 metres long and 207 bars that are 5 metres long.
(a) Model the problem as a linear programming problem.
(b) Solve the problem by graphical method.