Answer to Question #171771 in Statistics and Probability for Dinesh

Question

A medicine manufacturing company is trying to choose between two pharmaceutical companies that are competing in the market. First Company has offered the manufacturing company Rs 10,000 plus Rs 2 per medicine sold. Second Company has offered the manufacturer Rs 2,000 plus Rs 4 per medicine sold. The manufacturer believes that five levels of demand are as follows: 1,000, 2,000, 5,000, 10,000 and 50,000. Compute the payoffs for each level of demand for first company and second company. Construct a payoff Table, indicating the events and alternative courses of action. Construct a decision tree. Construct an opportunity loss Table

Answer 1

The payoff of the first company at the level of demand 1000 will be $10000+2\cdot 1000=12000$.

The payoff of the first company at the level of demand 2000 will be

$10000+2\cdot 2000=14000$.

At the level 5000 it will be 20000, at the level 10000 it will be 30000, at the level 50000 it will be 110000.

The payoff of the second company at the level of demand 1000 will be $2000+4\cdot 1000=6000$.

The payoff of the second company at the level of demand 2000 will be

$2000+4\cdot 2000=10000$.

At the level 5000 it will be 22000, at the level 10000 it will be 42000, at the level 50000 it will be 202000.

Payoff Table:

Decision Tree:

At the level of demand 1000 the optimum action is First company because at the level of demand 1000 the payoff of the first company 12000 is bigger than the payoff of the second company 6000. At the level of demand 1000 profit of optimum action is 12000.

The opportunity loss for the first company at the level of demand 1000 is 12000-12000=0. The corresponding value for the second company is 6000-12000=-6000.

The same calculations will be conducted for all the levels of demand.

Opportunity Loss Table: