Further Business Applications Lesson 6.3

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

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

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

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?

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

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

Sample Problem The LeTourneau Bookstore has an 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?

Assignment Lesson 6.3 Page 333 Exercises 5 – 13 odd

Elasticity of Demand What does change of price do to demand for the object? For essentials such as milk, fuel, etc. relatively small price changes do not change the demand For luxury items such as cars or jewelry, small percentage price changes can significantly change the demand Sale

Elasticity of Demand Sensitivity to demand to changes in price Where … Relative change Ratio of % change in demand to % change in price Where … Δq = change in demand Δp = change in price

Elasticity of Demand If we say that q = f(p) Demand is Then can be shown that E = Elasticity Demand is Inelastic if E < 1 Elastic if E > 1 Unit elastic if E = 1

Implications Total revenue is maximized at price where demand has unit elasticity Try q=48000 – 10p2 Find E Are there values of p at which total revenue is maximized? Total Revenue Price

Implications If demand is inelastic (E < 1) Total revenue increases as price increases If demand is elastic (E > 1) Total revenue decreases as price increases Total Revenue Price Total Revenue Price