Tommy & Lefebvre is Ottawa's full-line authorized dealer for Atomic snowboards for the 2020-2021 winter season. T&L's sales projections for November, December and January are 550, 800, and 300 snowboards for each of these next three months. Atomic has agreed to provide T&L with up to 650 boards each month at a unit cost of $82. Using "rush orders", Atomic can also provide T&L with up to 50 additional boards per month at an increased unit cost of $97 each. Boards not sold at the end of the month are stored in the T&L store at a cost of $20 per board per month. It takes the store clerks 0.5 hours per board to set up, sticker, and display the snowboards and clerk capacity is limited to 500, 600, and 400 hours in each of the 3 months respectively. Finally, T&L have 50 Atomic snowboards from last season (2020 model) that they can sell this year and they want to have at least another 75 snowboards (2021 model) left at the end of January.

Write down the algebraic/mathematical formulation of this problem as a linear programming problem to minimize the total cost to T&L of purchasing and stocking the snowboards.(Define the decision variables, objective function, and constraints). DO NOT SOLVE.