A shoe manufacturer received orders for 205, 215, and 210 pairs of shoes in September, October, and November, respectively.

The production line can manufacture a maximum of 200 pairs of shoes per month for $300 per pair on the regular time. An extra 15 pairs of shoes per month can be produced for $325 per pair.

Any unsold shoes at the end of the month will incur a storage cost of $20 per pair. The current inventory at the end of August is 10 pairs of shoes.

Show step-by-step to formulate this multi-period problem as a linear programming model that minimizes the total cost. Start with naming each variable.