Before unveiling the new iPhone15, the pricing manager at Apple was considering how much to charge for the new version and also how much to charge for the iPhone14, which is now an older model but still has a demand. Apple's marketing department has estimated that the demand for iPhone15 is P15 = 14 Q15 and for the iPhone14 is P14 = 10 Q14, where prices are measured in hundreds of dollars and quantities in millions of units (this means that the answer you will obtain at the end needs to be multiplied by 100 for the prices and 1,000,000 for the quantities). Apple's marginal cost of production is MC(Q) = Q, where Q = Q14 + Q15, and cost is measured in hundreds of dollars (so if you get, for example, that Q = 3, then MC is 300 hundred dollars). Find the optimal group pricing strategy for Apple. Obtain the price elasticities of the two groups at the pro t maximizing price-quantity combinations. (Hint: you need to solve two equations in two unknowns.)