A hot dog vendor must decide on Monday how many hot dogs to have available for the coming Saturday's football game.Each hot dog costs the vendor $3.00 and is sold for $5.00.After the game any unsold hot dogs are discounted and sold to the university cafeteria for $1.75.The vendor believes that the demand for hot dogs follows the probability distribution shown below: The optimal number of hot dogs the vendor should order for next Saturday's game is

Question

A hot dog vendor must decide on Monday how many hot dogs to have available for the coming Saturday's football game.Each hot dog costs the vendor $3.00 and is sold for $5.00.After the game any unsold hot dogs are discounted and sold to the university cafeteria for $1.75.The vendor believes that the demand for hot dogs follows the probability distribution shown below:  The optimal number of hot dogs the vendor should order for next Saturday's game is

Quizplus · Accepted Answer

The optimal number of hot dogs can be calculated by finding the point where the marginal cost and marginal revenue are equal. Marginal cost is the cost of producing one additional unit of output, while marginal revenue is the additional revenue generated by selling one more unit.

In this case, the marginal cost of each hot dog is $3.00, while the marginal revenue is $5.00 for the first 2000 hot dogs sold (as shown in the probability distribution table).

If the vendor were to order more than 2000 hot dogs, the marginal revenue would decrease to $1.75 (the price at which the remaining hot dogs are sold to the university cafeteria).

Therefore, ordering 2000 hot dogs is the optimal choice as it allows the vendor to maximize revenue while minimizing costs.

A Hot Dog Vendor Must Decide on Monday How Many