otal Lawn Care (TLC) is the only lawn care firm in Springfield. Demand for lawn care can be represented by the function P = 130 ? 2Q. TLC has constant marginal cost $ 10 and zero fixed cost for doing each mowing service, so it has the constant average cost of $10 per mowing.

TLC's profit = revenue - cost, namely ? = P Q ? 10Q

a) (6pts) What is the optimal output Q that TLC should sell? You can express profit in terms of only Q by substituting P = 130 ? 2Q for P. Then take its derivative with respect to Q and set the derivative equal to zero to solve for optimal Q.

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b) (1pt) What is the optimal price P that TLC should charge for each mowing service? c) (1pt) How much profit will TLC earn at the optimal price and output?

3. (8pts) (Monopoly) Total Lawn Care (TLC) is the only lawn care rm in Springeld. Demand for lawn care can be represented by the function P = 130 2Q. TLC has constant marginal cost $ 10 and zero xed cost for doing each mowing service, so it has the constant average cost of $10 per mowing. TLC's prot = revenue - cost, namely 71' = PQ 1062 a) (6pts) What is the optimal output Q that TLC should sell? You can express prot in terms of only Q by substituting P = 130 262 for P. Then take its derivative with respect to Q and set the derivative equal to zero to solve for optimal Q. h) (1pt) What is the optimal price P that TLC should charge for each mowing service? c) (1pt) How much prot will TLC earn at the optimal price and output