If you 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 6T² + 112I 6I² + 4TI. You have a budget of $25 that you can spend on T and I. The price of a TV commercial is $1/2 per unit and the price of an online commercial is also $1/2 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? 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?