13. A manufacturer makes three types of decorative lamps; model A, model B, and model C. The raw material requirement for all lamps is the same, but the cost of production differs due to different labour requirements. Each model A lamp requires 0.1 hr of assembly time, 0.2 hr of wiring time, and 0.1 hr of packaging time. Model B requires 0.2 hr of assembly time, 0.3 hr of wiring time, and 0.1 hr of packaging time. Model Crequires 0.3 hr of assembly time, 0.4 hr of wiring time, and 0.1 hr of packaging time. The manufacturer makes a profit of Rs 120 on each model A lamp, Rs 190 on each model B lamp, and Rs 210 on each model Clamp. The manufacturer can schedule up to 80 hours of assembly labour, 120 hours of wiring labour, and 100 hours of packaging labour.

Assuming that all lamps produced can be sold, determine the optimal quantity of each model and the shadow prices of each of the resources.

Write the dual of the given problem and use it for checking the optimal solution.