a. Write a linear optimization model (i.e., identify decision   variables, objective function and constraints) b. Use Solver in EXCEL to   solve the following problems and highlight the optimal solutions in your   Excel files.   Production   Planning. 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:    Standard Narrow Wide      Trimmer 0.2 0.4 0.6      Shaper 0.6 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 $8  $6  $10       What are the   optimal production quantities for the company? What is the pattern in the   optimal allocation?