ABCD company is an office equipment company that 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 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet 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 to national chains Shops.

Required:

Develop a linear optimization model to determine how many of each type of desk the ABCD company should make next week to maximize profit contribution [Assume: S = units of standard desk produced & D = units of deluxe desk produced. No need to solve the model, neither graphically nor by Solver: just develop the mathematical model for this part].