# Develop a linear mathematical optimization model

Problem: Burger Office Equipment produces two types of desks: standard and deluxe. Deluxe desks have oak tops and more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 sq. ft. of pine and 10 hours of labor, while deluxe desks require 60 sq. ft. of pine, 18 sq. ft. of oak, and 16 hours of labor. For the next week, the company has 5,000 sq. ft. of pine, 750 sq. ft. of oak, and 400 hours of labor available. Standard desks net a profit of \$150, while deluxe desks net a profit of \$320. All desks can be sold.

Develop a linear mathematical optimization model to determine how many of each desk the company should make next week to maximize profit contribution.

Implement your model on a spreadsheet and find an optimal solution using Solver.

Explain the reduced cost associated with standard desks.

What constraints are binding?

If 25% of the oak is determined to be cosmetically defective, how will the optimal solution be affected?

The shop supervisor has suggested that his workers be allowed to work an additional 50 hours at an overtime premium of \$12/hr – is this a good idea? Why or why not?

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