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 meter lengths; or
(ii) Whether to cut it into one 2 meter length, one 3 meter length and one 5 meter length.
In the next week the company requires 105 bars that are 2 meters long, 153 bars that are 3 meters long and 207 bars that are 5 meters long.
(a) Model the problem as a linear programming problem.
(b) Solve the problem by graphical method.