A company requires two types of components (A and B). The factory incurs a fixed cost for erecting a order for any of the $ 800 components, plus a fixed price of $ 30 and $ 45 per order of each component, and the cost of the units is $ 180 and $ 100 respectively. Annual demand is 2,000 units for product A and 2,500 units for product B. The annual cost of interest, insurance and taxes on average inventory investment is 10% of the average inventory value. The company does not have a lot of cash flow for what they have defined not to exceed the budget of 100.00 in inventory value in any moment. The company has determined that due to the obsolescence of the material, the average inventory of product B it should never exceed 200 units. Determine the lot sizes that minimize the total cost function, considering that product A allows shortages and the penalty is $ 550 unit / year. a) Formulate the problem as a mathematical programming model (objective function and restrictions) that minimize total annual cost. (10pts) No solving required, just formulation. b) Represent the problem in a single equation including the restrictions in terms of lambda (10pts) No solving required, just formulation. c) Find the optimized lot sizes (10pts). They can make use of Excel for the solution and point to the answer