Problem 3 (35 pts). To model the influence of price on customer purchase probability, the follow- ing logit model is often used (p is the price, (p) is the purchase probability): (p) 1+e-p Assume the cost of the product is 0 (e.g., cellphone apps). As the seller, you want to maximize the expected revenue by choosing the optimal price. That is you want to solve: max, p(p) 4. Here is another way to transform the original problem into a convex problem. If we take a log of the objective function, namely log(pX(p)). Show that the new objective function is concave, and then the problem max, log(pX(p)) becomes a convex optimization problem. 5. (Optional) Use CVX to solve this convex problem. Here you may use the following form when inputting into CVX. Problem 3 (35 pts). To model the influence of price on customer purchase probability, the follow- ing logit model is often used (p is the price, (p) is the purchase probability): (p) 1+e-p Assume the cost of the product is 0 (e.g., cellphone apps). As the seller, you want to maximize the expected revenue by choosing the optimal price. That is you want to solve: max, p(p) 4. Here is another way to transform the original problem into a convex problem. If we take a log of the objective function, namely log(pX(p)). Show that the new objective function is concave, and then the problem max, log(pX(p)) becomes a convex optimization problem. 5. (Optional) Use CVX to solve this convex problem. Here you may use the following form when inputting into CVX