Problem
Katie likes to paint and sit in the sun. Her utility function is U(P,?S) = 3PS + 6P, where P is the number of paint brushes and S is the number of straw hats. The price of a paint brush is $1 and the price of a straw hat is $5. Katie has $50 to spend on paint brushes and straw hats.
a. Solve Katie's utility-maximization problem using a Lagrangian.
b. How much does Katie's utility increase if she receives an extra dollar to spend on paint brushes and straw hats?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.