Optimization in Business Economics Life Sciences Lesson 4.7

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

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

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

Minimum Average Cost Try for our previous example

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

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?

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

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

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

Optimal Holding Time

Assignment Lesson 4.7 Page 259 1 – 39 EOO