ABC will produce 3 products and knows that each startup generates a cost of 5,000 pesos. The cost of the units is $ 20, $ 15 and $ 10 respectively. Annual demand is 100,000 units for Product A, 150.00 units for Product B, and 200,000 units for Product C. The inventory rate is 15% per month. Product A and B are perishable and their average inventory must not exceed 10,000 units. The company seeks an acceptable return on investment so they should not exceed the budget of 100,000 in inventory value at any time. The available space in warehouse is 500m3 and product A occupies 1.5m3, product B 0.5m3 and C 2m3. Consider that product A and B allow shortages and the goodwill loss cost is $ 3 for each unit.

Formulate the problem as an optimization model (objective function and constraints) that minimizes the total annual cost. In terms of Q.