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 batches per 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 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?

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

10. 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

11. 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

12. 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

13. 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

14. 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