II. (16 pts) Meg and Tim invested $30,000 in the design and development of a new revolutionary product which they can manufacture for $3 per unit. From a careful market study, they determined that if they spend Sa on advertising and sell the product at $p (per unit), then they will sell a total of 2500 + 5va - 30p units of the product. Meg and Tim want to develop an optimization problem that would maximize their profits for this new product. Question Answer Pts 1. Formulate the appropriate objective function as a function of a and p. 2 2. Set up the system of equations needed to identify the optimal price and level of advisertising. 2 3 . What are the optimal price and. a: p: level of advertising? 3 4. Formulate the Hessian 3 5. Principal Minor Determinants of the Hessian 3 6. Conclusions about the Hessian and Indicate whether it is a 1 Minima/Maxima 7. Total Profit 2 S_Scanned with CamScanner