3. A new startup wants to test drive their amazing new product (edible laundry pods!) next summer. The have a forecast for the demand (d1, d2, d3) and the production costs (c1, c2, c3) for each of the three months in the summer. They have a limited production capacity of K units per month but they can also outsource up to M units of additional production each month at a cost of p dollars. Initial inventory is 0 and final inventory must be 0 at the end of the summer. They have virtually unlimited capacity to store units in inventory at a cost of h dollars per unit stored per month. The goal of the company is to create a production, outsourcing, and inventory plan to satisfy the demand at minimal cost. Formulate as a mathematical program, clearly state your variables, objective function, and constraints.