The monthly investment in the purchase of materials to manufacture a certain product is equal to 10 times the square of the number of units manufactured of this product. In addition, monthly manufacturing costs are $/2,000 per unit manufactured plus a fixed cost of $/250,000 for infrastructure implementation, maintenance, and services. On the other hand, it is known that it is always possible to sell everything manufactured per month and the unit sale price of the product is $8000. a) Plot the monthly cost, revenue and utility functions in terms of the number of units manufactured, indicating their domains and their respective ranges. b) Find the maximum profit and the number of units manufactured to maximize the monthly profit