Question

A company produces boxes of diet cereals and standard cereals. If a customer’s last purchase was a diet cereal then the next purchase will also be diet cereal with probability 0.95. However if the customer’s last purchase was a standard cereal, then the next purchase will also be a standard one with probability 0.8. Suppose that the respective costs are 160 cents, 150 cents and the respective prices are $2.5, $2.0 for diet and standard types.

a) If 10 000 cereals are sold per month, what is expected profit for standard cereal?

b) If the company sells diet cereal at a price of (180-x) cents where 15 £ x £ 20, then (0.8 + x /100) of customers whose last purchase was diet type will buy diet again. For what value of x company maximizes profit?

£ is <=

Answer 1