Let each option be solved separately and I want a solution without excel.

4. The FCC Cafeteria, a fast lunch spot in ankaya University campus, purchases several basic cooking ingredients from a supplier. The annual usage (demand), purchasing cost, and setup (order) cost of these ingredients are given in the table below. The inventory carrying rate is 0.10 per unit per year. Ingredient 1 2 3 4 Annual Demand (in units) 100 100 200 100 Purchasing Cost ($ / unit) 10 40 10 10 Setup Cost ($ / order) 2 2 4 3 (a) Assume that all ingredients are ordered independently. For each ingredient, determine the optimal cycle time and order quantity. Calculate the associated total cost of all ingredients. (b) Assume that all ingredients are ordered independently, and the cafeteria management wants to limit their annual inventory holding cost by $52.5. Using Lagrange multiplier technique, determine the optimal cycle time and order quantity for each ingredient. Calculate the associated total cost of all ingredients. (c) Assume that all ingredients have a fixed (common) order cycle. Determine the optimal cycle time, the order quantity for each ingredient, and the associated total cost. Draw a figure that illustrates the change in inventory levels of the ingredients