Hotdogs. End of story.

It seems our IT specialist has done an excellent job by applying a mathematical model to optimize the profit from selling hot dogs.

Using the following equations:

Sales Model

qtE=b0+b1∗pt+b2∗at+b3∗at2

Profit Model

profit=h(pt,at)=qtE∗(pt−2)−at

where qtE represents the expected number of sales, pt is the price, at is the advertising expenditure, and 2 is the cost price of hot dog.

Based on the estimated parameters, which can be found in the previous post, the optimal values were calculated as follows:

Price of a hot dog (pt): 7.04 monetary units

Advertising expenditure (at): 272 monetary units

These values were derived by calculating the first derivatives with respect to pt and at, and further analyzing the Hessian,

which turned out to be negatively definite, indicating a maximum profit under these conditions.

The results are visualized in the space Г: (pt,at,profitE)(pt,at,profitE), providing a clearer understanding of the optimization.

This is a superb example of employing mathematical methods to make business decisions.

I wish our IT specialist continued success in their research and sales optimization!