Further Business Applications

1. Further Business Applications Lesson 6.3

2. Economic Lot Size • A manufacturer can produce its product in varying batch sizes • 120 once a year • 60 twice a year • 10 each month … etc. • Elements to be considered • k = Costs for storage one unit for a year • f = Fixed setup cost per batch • g = Mfg. cost per item • M = Total number of items per year • q = Number of items per batch

3. Economic Lot Size • Manufacturing cost per batch • Number of batchesper year • Total annual manufacturing cost • Inventory goes down linearly q to 0 • Average inventory q/2 units per year • Storage costs

4. Economic Lot Size • Total production cost is sum of • Manufacturing costs • Storage costs • To minimize T(q) we solve T '(q) = 0 for q • Find this solution before proceeding • Check your answer with text book solution

5. Try It Out • LeTourneau Lamps makes 100,000 lamps annually • Costs $1 to store a lamp for a year • Costs $500 to set up factory to produce a batch • What is the optimum number of lamps to produce in each batch?

6. Economic Order Quantity • Suppose we purchase an item for sale • How often should we order • How many do we buy for each order • Elements to be considered • k = Costs for storage one unit for a year • f = Fixed costs to place an order • M = Total number of items per year • q = Number of items per batch • Goal: minimize Total Cost = Storage Cost + Reorder Cost

7. Economic Order Quantity • Assume average inventory of q/2 • Yearly storage cost • Number of orders placed annually • Reorder cost • Total cost Determine T '(q)Solve T '(q) = 0 for q

8. Sample Problem • The LeTourneau Bookstore hasan annual demand for 100,000 copies of that best seller, Calculus with Applications • It costs $.50 to store the copy for one year • It costs $60 to place an order • What is the optimum number of copies per order?

9. Assignment • Lesson 6.3 • Page 333 • Exercises 5 – 13 odd