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

To find the optimal number of hot dogs we need to find the point where the expected profit is maximized. Let's calculate the expected profit for each option:

For 1000 hot dogs:
- Expected demand = 400 hot dogs
- Expected revenue = 400*$5 = $2000
- Expected cost = 1000*$3 = $3000
- Expected profit = $2000 - $3000 = -$1000

For 1500 hot dogs:
- Expected demand = 600 hot dogs
- Expected revenue = 600*$5 = $3000
- Expected cost = 1500*$3 = $4500
- Expected profit = $3000 - $4500 = -$1500

For 2000 hot dogs:
- Expected demand = 800 hot dogs
- Expected revenue = 800*$5 = $4000
- Expected cost = 2000*$3 = $6000
- Expected profit = $4000 - $6000 = -$2000

For 3000 hot dogs:
- Expected demand = 1000 hot dogs
- Expected revenue = 1000*$5 = $5000
- Expected cost = 3000*$3 = $9000
- Expected profit = $5000 - $9000 = -$4000

As we can see, the expected profit is negative for all options. However, we should choose the option that gives us the smallest loss. Therefore, the best option is to order 2000 hot dogs, which gives us an expected loss of $2000. Ordering more hot dogs would only increase our losses.

A Hot Dog Vendor Must Decide on Monday How Many