5. For the following parts (a-g), use the following prompt: A tech company produces a budget smartphone which costs $45 to produce each unit. The company also has a fixed cost of $15,000 per month, meaning the cost function is C(x) = 45x+15,000 The price function for this phone is p = 300 - 0.5x, where p is the price at which exactly x phones are sold. The company must make at least 200 units. a. (2 points) Construct the revenue function for this manufacturer. b. (2 points) Construct the profit function for this manufacturer. c. (3 points) How many phones must be sold to maximize profit for one month? d. (2 points) What is the maximum profit for one month? c. (2 points) How do you know that the value you found in part e is a maximum? Prove it by using a 1" or 2d derivative test or using the process from section 14.1. f. (3 points) What is the maximum revenue for one month? g (2 points) How do you know that the value you found in part g is a maximum? Prove it by using a 1" or 2nd derivative test or using the process from section 14.1.