The Bogard Corporation produces 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 packaging. All three types require 0.4 hours of assembly time, but the machining operations have different processing times, as shown in the following table, in hours per unit:

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:

a. What are the optimal production quantities for the company?
b. What is the pattern in the optimal allocation?

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Standard Standard Wide Narrow Trimmer 0.2 0.4 0.6 0.5 Shaper 0.2 0.6 Standard Wide Narrow Profit $10 $8 $6