For a certain company, the cost function for producing :13 items is C (at) = 30:13 + 250 and the revenue function for selling :1: items is Rte) 2 U'.5[a: 80)2 | 3,200. The maximum capacity of the company is 130 items. The prot function 13(3) is the revenue function Rte) (how much it takes in] minus the cost function C (3:) (how much it spends}. In economic models, one typically assumes that a company wants to maximize its prot, or at least make a prot! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the prot function? P (at) = IQ E - Hint: Prot = Revenue - Cost as we examined in Discussion 3. 2. What is the domain ofP(:1:)? Hint: Does calculating P{a:) make sense when a: = 10 or :1? = 1, 000? 3. The company can choose to produce either 50 or 60 items. What is their prot for each case, and which level of production should they choose? Prot when producing 50 items = Number Prot when producing 60 items = Number 4. Can you explain, from our model, why the company makes less prot when producing 10 more units