1. Production Planning. The Bogard Corporation pro¬duces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packa-ging. All three types require 0.4 hours of assembly time, but the machining operations have different processing times, as shown below, in hours per unit:
Standard Narrow Wide
Trimmer 0.2 0.4 0.6
Shaper 0 0.2 0.5
Each machine is available 150 hours per month, and the current size of the assembly department provides capacity of 600 hours. Each bookcase produced yields a unit profit contribution as follows:
Standard Narrow Wide
Profit $a $6 $10
a• What are the optimal production quantities for the company?
b. What is the pattern in the optimal allocation?