1. Optimization in Business Economics Life Sciences
Lesson 4.7

2. Maximizing Profits Profit = Revenue – Costs
Profits are maximized when:

3. Maximizing Profits Try this:
How many items should we make and sell to make the most profit?

4. Minimum Average Cost Average cost :
This is minimized when marginal cost is equal to average cost.

5. Minimum Average Cost
Try for our previous example

6. Application Consider balancing shipping versus inventory costs
Total cost = storage cost + ordering cost + item cost
Shipping
Inventory
ordering
freight
handling
storage
We seek to minimize this function

7. Example Selling 600 cans of hairspray per year Assume
cost $4 each
shipping $30 per shipment
storage $0.90 per can per year
Assume
uniform sales throughout year
each shipment arrives as preceding used
How frequently should shipments be ordered to minimize costs?

8. Hairspray Orders Let x = number of cans ordered each time Storage cost
Ordering cost
Item cost

9. Optimal Holding Time Consider an asset that increases in value
There may be a point in time when better to sell
This is when present value …
at current rate of interest
is maximized
Given V(t) = price t years from now
Present value P(t) = V(t) e-r*t
Where r = annual interest rate t = years

10. Optimal Holding Time Given : r = 10% = 0.10
When is the best time to sell
P(t) = ?
P`(t) = ?
Maximum when x = ?

11. Optimal Holding Time

12. Assignment
Lesson 4.7
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