This is an Intermediate Microeconomics question. We are stumped. Can someone please help. Thank you.

Your own a chocolate producing company which can advertise on both television (T) and internet (I). The effect of TV and online commercials on sales is again given by S(T, I) = 500 + 48T - 672 + 1121 -612 + 4TI. You have a budget of $25 that you can spend on T and I. The price of a TV commercial is $, per unit and the price of an online commercial is also $, per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss