6. (6pts) Perfect Competition: You are an olive oil maker. Your prod. function is: q = 120K 1/sz + 80L 1AL2 and the price of your olive oil is $5. Capital equipment costs $10 and labor costs $5. a) (3pts) Create a prot function for your olive oil business. If you are unconstrained in your production budget, what is your prot-maximizing use of capital, K* and labor, L* in the long run? (when all inputs are variable.) What are your prots? b) (3pts) Now assume that your production budget is constrained to $4000, which you must allocate between capital and labor. Set up a constrained Lagrangian prot maximization problem. What are your new optimal levels of K and L? (K* and L*) What are your prots