Suppose you are given a budget of $V million and are tasked with maximising the number of pre-orders. It costs $1000 to rent a billboard and $C million to sign a celebrity spokesperson. Finally, suppose

g(b,s) =b^1/2 +2500s^1/4

where b is the number of billboards rented and s is the number of celebrity spokespeople signed.

1. Write the constrained maximization problem

2. Can the inequality constraint hold with strict inequality? Justify your answer using a complementary slackness argument.

3. Relate your answer in part 2 to the interpretation of the Lagrange multipliers value

4. Find the equation relating the optimal number of celebrity spokes people to hie with V and C

5. Holding everything else fixed, how does the optimal number of spokespeople change in C ,eg. What is s(C)? Interpret its sign