L 'Oreal, a French cosmetics rm, recently acquired the 30052 Shop, an US. body care products company known for its ethical production of cosmetics. It is expected that this acquisition will make consumers look more favorably at all L 'Oreal products, boosting their demand. To examine whether L 'Oreal made the correct decision, assume the following information to answer the questions 16-20 below. A. Inverse Demand for L 'Oreal products without acquisition: P = 20 2Q. B. Inverse Demand for L 'Oreal product with acquisition: P = 200: - ZQ, where a is a parameter greater than 1, representing the boost in demand. C. Constant marginal costs of 4, regardless of whether L 'Oreal makes the acquisition or not. D. An acquisition cost of 20 if L 'Oreal makes the acquisition. 1. (6 points) Set up L'Oreal's prot function if it does not make the acquisition. Evaluate the rst-order conditions and solve for the optimal quantity (QM). 2. (6 points) Set up L'Ol'eal's prot function if it does make the acquisition. Evaluate the rst- order conditions and solve for the optimal quantity (QA*). 3. (6 points) Suppose that the acquisition would mean that the parameter 0!. takes the value of 1.2. Using the available information, show whether L'Oreal made the right decision by acquiring the Body Shop. Did they make the right decision? 4. (3 points) Given your calculations above, what's the maximum xed cost that L'Oreal would be willing to pay for the acquisition